Heat the oven to 350 degrees Fahrenheit and place the rack in the middle of the oven. Fill a miniature muffin pan with foil liners. Peel cooled sweet potatoes and run flesh through a potato ricer, or mash until very smooth. (Do not blend in a blender or food processor.) Measure 1 ½ packed cups (about 12 to 13 ounces) from sweet potato mash; you may have a little extra, which you should warm up with a pat of butter and sprinkle of sea salt and not share with anyone. Whisk flour, baking powder, baking soda, salt, and spices together in a medium bowl. In a large bowl, beat butter and brown sugar together with an electric mixer until light and fluffy, about 2 to 3 minutes. Add vanilla and eggs, and beat until just combined. Mix in sweet potato puree, then stir in dry ingredients just until they disappear. Spread batter in prepared muffin pan, and bake cupcakes until a toothpick inserted into the center comes out clean, about 15-20 minutes. Let cupcakes rest in pan for 5 minutes on a cooling rack, then remove onto cooling rack, and let cool completely. You can speed this up, as I always do, in the fridge.