To start, prick your sweet potato all over with a fork. Wrap in foil and roast at 400ºF until tender (45-60 minutes) OR peel, cut in cubes, and simmer on low until tender. When cool enough to handle, scoop out the flesh and mash with a fork.
To make the cupcakes:
Preheat oven (or reduce temperature) to 350ºF. Line a standard 12-cup muffin tin with paper liners.
Add sweet potato to a medium bowl and whisk in brown sugar, oil, eggs and vanilla extract to fully combine.
In a second large bowl, whisk together the flour, spices, baking powder, and salt. Add the sweet potato mixture and stir with a large spatula until just combined (don't overmix).
Divide batter among prepared muffin cups by filling each cup about half full. (If there's extra batter, go back and top them each up a little spoonful at a time to make them even).
Bake for 18-22 minutes, rotating pan once halfway through, until internal temperature reaches 190ºF. Cool on wire rack.
To make frosting:
Bring 1" of water to a strong simmer in a small saucepan. Combine egg whites, sugar and cream of tartar in a large heat-proof bowl set over top (or in a double boiler). Make sure your bowl does not touch the water.
With burner heat on low, beat with hand mixer until stiff, very glossy peaks form, about 7 minutes. Remove bowl from heat and beat in vanilla extract.
Pipe or spread frosting onto cupcakes (unlike with other frostings, they don't have to be completely cooled), then carefully toast with a kitchen torch or place frosted cupcakes on a baking sheet broil for 1-1 1/2 minutes (watching very closely).
Video
Notes
Be sure to buy orange sweet potatoes, not yams (which are either brown or purple on the outside and white and starchy on the inside). See photo example in blog post.
Sweet potatoes lose moisture (and thus weight) when water escapes as steam while they cook. To ensure moist cupcakes, minimize the steam loss by wrapping the sweet potatoes tightly in foil before roasting, or cook them cubed in simmering water. The weight of raw sweet potato to yield 1 cup mashed is therefore an estimate, as the moisture loss varies.
I highly, highly recommend you weigh your flour to ensure moist cupcakes every time. A bit too much flour added by inaccurately measuring by volume can make ANY cupcake recipe dense and dry.
If you do not have a kitchen scale, make sure you fluff your flour in the bag, then lightly spoon it into the measuring cup and level it off.
Check for doneness using a thermometer, not a toothpick. This ensures the cupcakes come out of the oven as soon as they are finished baking. Over-baking is another reason why cupcakes turn out dry.
Don't overmix the batter once the liquids are added. The more you mix, the tougher cupcakes become. The goal is to just combine.
FROSTING TIPS
If you have a gas stove, make sure to keep the flame low. You don't want the bottom of the bowl to touch the simmering water OR the direct heat of the flame.
Dampen a paper towel with vinegar and wipe down bowl and beaters before you start. Rinse completely with water and then dry with a clean dish towel. This ensures no oil residue is leftover from previous baking. Any trace of fat can stop egg whites from whipping up.
If you don't have a kitchen torch you can toast the frosted cupcakes by placing them on a baking sheet and placing them under the broiler very briefly (and watching VERY carefully).
You may frost the cupcakes with whipped cream and dust them with ground cinnamon for a super simple frosting option.