Carrots get sweeter if they are left in the garden till after the ground freezes (generally under mulch to facilitate winter digging.)
Then again, I personally consider cooking carrots a good way to ruin them, as I find them far better raw.
cooking.stackexchange.com/users/34242/Ecnerwal
There are many recipes for glazed carrots Google - glazed carrot recipes .
Generally using brown sugar or honey and butter, sometimes adding additional flavorings such as orange, bourbon or herbs.
cooking.stackexchange.com/users/35357/Debbie M.
There are varieties of carrots that have been bred for extra sugar, but you won't find them in your typical grocery store.
Most of the grocery store carrots have been bred for color, shape, production and storage.
In grocery stores that sell loose carrots, you can sometimes find 'winter carrots'.
They're quite large (nearly 2" / 5cm across).
These are carrots that have been left in the ground over the winter -- they are typically much sweeter than carrots that are taken out of the ground in warmer weather.
I have seen larger carrots at the latin markets and restaurant supply stores near me, but I've never done side-by-side taste tests to confirm if these are sweeter than standard grocery store carrots.
There are also seed companies (eg, Baker Creek , Burpee , Johnny's , Territorial , etc.) who sell varieties bred specifically for their sugar content, much like what's being done with corn.
If you grow your own, you can seek these out, or you can check to see if any of the farmer's markets near you carry them.
Much like heirloom tomatoes, they're often a bit stranger in color and shape than what you get in the grocery stores -- they might be short and stubby, or have a dramatic taper that isn't useful to make 'baby carrots')
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While some carrot varieties are naturally woody in taste most carrot varieties have a natural sweetness to them, especially when they are well grown and fresh.
While I'm not on the organic band-wagon this is one case where I've found that buying organic does generally get you a better product as the carrots are grown better and allowed to mature, most cheap store carrots are picked before the sugars develop.
The best carrots I ever had were fresh from someone's garden, they were amazingly sweet, almost sugary.
I haven't had much luck growing them myself - in dense clay soil
they end up looking like nuclear mutants -
but I will try again as the result was amazing.
cooking.stackexchange.com/users/19707/GdD
I find that there actually are (or maybe I got lucky as my sample size has been small...
).Where
I live there is a type of carrot that is usually sold massive in size
, it is around 2"-3" in diameter at the stem-end of the carrot
and it stays fat and thick all the way to the tip (usually about a foot long).
Some of the larger grocery stores carry them but the asian markets all have them too.
(In the normal grocery stores they are nearer to the things like bok-choy than to the rest of the carrots.
Growing up, larger carrots were always bitter and woody but the few carrots I have tried from whatever this variety is have always been abnormally sweet and very tender.
cooking.stackexchange.com/users/36737/BunnyKnitter
These days I am trying to get my wife to eat her carrots. Usually we are just boiling them, and adding some spices and butter.  But she swears that she used to eat sweet carrots, but she can't say how long ago. Supposedly I should know the difference, but I don't recall such a thing. It must be that my sense of taste is weak.  In any case, is there a sweet variety of carrots? Or is there a common recipe to sweeten them up?
Is there such a thing as "sweet" carrots?
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Some varieties of carrot are naturally sweeter than others, but in general they will be sweeter if left to mature in the ground, especially after the first frost. Organic carrots are more often allowed to mature like this and may be sweeter, or you can find speciality stores that sell sweeter varieties harvested or as seeds. There are also recipes for glazed carrots that are artificially sweetened. Some varieties of carrot have been specially bred to be sweeter. However, normal carrots left in the ground longer or home grown and organic carrots tend to be sweeter that store-bought carrots. To sweeten ordinary carrots up use a recipe like glazed carrots.
Carrots that stay in the grounf longer and home grown and organic carrots tend to be sweeter. There are many recipes for glazed carrots which are quite sweet. Some varieties of carrot have been bred to be sweeter.