I want to make ginger drinks (bourbon, hot tea, ginger ale). In all cases, I want to create a ginger syrup that I can then add to bourbon, hot water, soda water to get my desired drink. I have tried the following methods:   Slice ginger thinly, put in boiling water for 1 hour Chop ginger very finely, bring water to boil, cover, steep one hour Chop ginger very finely, bring water to simmer for one hour Puree ginger and small amount of water in vita mix   In all cases, I've found that I need to remove the leftover ginger, as it would just settle out of a drink. I've tried it with varying amounts of sugar (from none to 1:2 sugar:water). What I'm left with is a pretty good product, but the ginger has a lot of flavor left in it. In fact, I can use it again with the same process and still get a good result.   I would like to get a very strong product with minimal life left in the ginger, so that I can minimize the amount of ginger I use. I'd also like the syrup / extract to be as strong as possible to minimize the amount I add to my drink. To top it off, I would prefer the process not be to laborious or time consuming.   How can I maximize the extraction of ginger flavor in to a liquid? 
Do you want the flavor of raw ginger, or cooked ginger flavor? Ginger contains several not very water soluble flavors, some of which are converted by cooking into different not very water soluble flavors.  To maximize flavor, you want the ginger mashed as finely as you can make it. That increases the surface to volume ratio of the stuff which in turn maximizes extraction.  Whether you cook or not, consider adding some alcohol, vodka should work, say 20-50% by volume to the mash, or the mash after it is cooked and cooled, and letting things steep overnight. The alcohol should increase the efficiency of extraction of the not very water soluble flavor oils. Filter afterwards of course, a coffee filter and a collander will work for that if you're not in a hurry, perhaps with a cheese cloth step to catch most of the bigger chunks. 