A scout on the trek between Gich and Chenek Henry Wismayer

My new companion on the mountain ledge emitted a croak and hopped a little closer. A momentary standoff followed as I contemplated a beak like bolt-cutters and talons the size of butcher's hooks. The ground dropped away for a vertical mile on either side of this slender promontory. This was no place for wrangling with a feathered brute. I shuffled back to let the enormous raven—twice as big as any I'd ever seen—scavenge from my picnic leftovers.

If you've ever wondered how Jack felt on that first foray up the beanstalk, you could do worse than to visit Ethiopia's Simien Mountains. Looming high above the volcanic outriders of the Great Rift Valley, 670 miles north of Addis Ababa, the range is nature junked-up on growth hormones: a 37-mile-long basalt escarpment staggered between altitudes of 10,000 and 15,000 feet. The area is populated by supersize plants, boisterous monkey armies 500-strong and supersize ravens with a penchant for cookie crumbs.

It's not a place that has always welcomed outsiders. From 1983 to '99, famine and regional warfare snuffed out its tourism potential. Today, however, with Ethiopia's economy expanding amid a semblance of political stability, the country is becoming a relatively safe and accessible destination. It's often the tawny grandeur of the Ethiopian highlands, cradling Lalibela's rock-hewn churches and towering above the fabled tombs of Aksum, that most impresses visitors. And it's here in the Simiens that this region can be seen at its biggest and most sensational. Inscribed as a World Heritage Site in 1978, it is a place that has been extolled by Unesco as "one of the most spectacular landscapes in the world." When I'd prepared to leave the scruffy, one-road town of Debark to begin a six-day trek of its high plateaus, I found myself wondering whether the hyperbole had left me expecting too much.

Trekkers on the escarpment rim above Chenek camp in the Simien Mountains National Park Henry Wismayer

From the moment I set out from the trailhead in the company of Dawoud Suleyman, my garrulous and experienced guide, all such concerns fell over the cliff. The terrain was relatively easy on the knees—sometimes pancake-flat. Yet the surroundings were on a scale that was hard to comprehend: giant lobelias (plants that look like a Dr. Seuss invention, with their spiky fronds and 10-foot-high flower stems) covering oceans of grass, a waterfall plummeting for hundreds of feet before disintegrating into clouds of vapor, squadrons of huge raptors in the sky.

It was dawn on the second morning when the region took its star turn. Two minutes out of the Gich camp, one of three rudimentary camping grounds that punctuate the plateau, a few slender silhouettes on a nearby outcrop heralded the first of what would be many encounters with gelada, the shaggy-haired, vegetarian monkey that is one of the best-known species to come out of Ethiopia.

The Simiens can be visited year-round, but a trip during Ethiopia's main dry season, running from October to February, is recommended. Henry Wismayer

Even the most cursory research will tell you that you are bound to meet gelada in the Simiens, but nothing prepares you for their numbers. Gelada are known to live in the largest aggregations of any primate, and this group lived up to its billing and quickly grew. Soon I was standing in mute astonishment as a chattering mob of 200 or so monkeys headed toward us. The alpha males, sporting leonine incisors and rock-star manes, led the group toward the direction from which we'd come. The rest of the herd followed in a flurry of barks and snuffles, barely paying us a second glance.

Half an hour later, their ruckus was still receding as we headed east over ground made spongy by the previous night's rain. The sun was still just a smear on the horizon when we arrived at the escarpment rim.

Slithering out onto a spine of rock, the trail had arrived at the park's most famous viewpoint: a knuckle of boulders known as Imet Gogo. I looked north from its 13,000-foot apex and saw a pair of incisor rocks standing in sharp relief against the sky. A sweep of arid plains rose up in the haze into ranks of weathered buttes and mountains, the remnants of ancient lava chimneys from which these highlands burbled forth 70 million years ago.

There, all within an hour of sunrise, was the essential canvas of a trek in the Simiens: unforgettable wildlife encounters set against the eye-popping backdrop of the escarpment rim. The vignettes had come so thick and fast that they'd left me dizzy. Now, lying on my belly to quell the vertigo, three bearded vultures pulled figure-eights overhead—Discovery Channel live, and on-demand.

Gelada monkeys Henry Wismayer

Some of the park's inhabitants are more ubiquitous than others, but on the third morning we caught sight of the most elusive of all. "Ethiopian wolf!" rasped Dawoud, pointing at a lanky canine shadow slinking across the frosty tundra, one of only 550 of his species still alive in the wild.

It was an auspicious start to a day spent mostly on the move—at 11 miles, it was our longest kick. From Imet Gogo, the trail turned south, first passing over a golden prairie rumpled with the headwaters of a phantom stream, then climbing through a gnarled forest of heather trees, where the rains had unleashed the scent of wild thyme. By noon we were back among the high grasslands, where some child-herdsmen hawked cow-horn goblets and eucalyptus crooks to the trekkers.

The clouds grew dark and ragged and we scurried to beat the rain. Soon we were at Chenek camp: a few ranger huts strewed along a rock-shelf and two open-sided shelters positioned on a slope beside a stream. For some trekkers, this is just base camp for the onward push to Ras Dashen, Ethiopia's highest peak at 15,000 feet. There seemed little point in pushing higher. We spent the last couple of days doing shorter walks, skirting the crags that clambered eastward and scouring the cliffs for rare glimpses of walia ibex, a mountain goat with extravagant scimitar horns that is found nowhere else, and was the last creature on our Simiens checklist.

On the final afternoon, Dawoud came running into camp. "Come and see," he said. "The ibex…more than 20 have come right into camp to graze."

Another unforgettable scene awaited us. Except, by now, I wasn't surprised at all.

The Lowdown: Simien Mountains National Park, Ethiopia

Getting There: Several major airlines reach the Ethiopian capital, Addis Ababa, via Europe. Hourlong flights on Ethiopian Airlines leave daily from Addis Ababa for the medieval fortress town of Gondar, and then it's a 50-mile bus ride to Debark, the jumping-off point for the Simien Mountains National Park. Visas are required for U.S. citizens, and are available upon arrival at Addis Ababa's Bole International Airport. A one-month, single-entry tourist visa costs $20.

Trekking There: The Simiens can be visited year-round, but a trip during Ethiopia's main dry season, running from October to February, is recommended. Travelers can hire guides and rent equipment at the National Park office in Debark. All visitors must pay an entrance fee ($6 per day), and are required to hire a scout ($4 per day). Addis Ababa tour company Ethiopia Uncovered can arrange personalized treks with renowned local guide Dawoud Suleyman. Five-day treks start at $800 and include accommodation and transfers to and from the capital.

Staying There: Billing itself the "highest hotel in Africa," Simien Lodge sits 10,700 feet above sea level on the western edge of the park. Solar-heated rooms in brick-walled roundhouses come with en suite bathrooms (from $152 per night). Debark's budget options include the Giant Lobelia Hotel (251-581-170-566), offering basic rooms for $15-$25 per night.

What to Bring: Tents and sleeping bags can be rented through the National Park headquarters in Debark, but the quality is basic; consider bringing your own. Sturdy footwear, rain gear and a mix of lightweight and warm clothes will help you cope with the fluctuating weather conditions. There is nowhere to buy food in the National Park, so stock up on supplies in Gonder or Debark.