In a large bowl, whisk together your dry ingredients (flour, sugar, cinnamon, ginger, baking soda, and baking powder) until they're well mixed.
In a separate bowl, whisk together you wet ingredients (melted butter, egg, milk, sweet potato puree, and vanilla extract) until lump free.
Pour your wet mixture into your dry mixture, and whisk until a thick, lump-free batter forms.
Pour (or better yet, pipe) your doughnut batter into a well-greased doughnut pan, and bake at 350F for 9-11 minutes, or until a toothpick inserted into the doughnuts comes out clean.
Let your doughnuts cool for about 5 minutes before turning them out onto a cooling rack.
Once the doughnuts are cool enough to handle, dip the side that baked down inside the pan (this is usually the moister of the two sides) into a little sugar to garnish.
Notes
Use a piping bag to pipe your doughnut batter into your doughnut pan. This is a lot easier and less messy than trying to pour from the bowl.
Doughnuts are easiest to remove from the pan while they’re still warm. The sweet spot seems to be about 2 and 5 minutes after they come out of the oven. Simply turn the pan over and gently shake it until the doughnuts come out (hot-pads are a good idea).
Leftovers: Baked doughnuts don’t keep well and tend to dry out faster than the fried variety. If you end up with leftovers, the best way to store them is in a paper bag. Whatever you do, don’t refrigerate them or put them in plastic.
Reviving stale doughnuts: If you wound up with leftovers and they’ve gotten stale, no worries! You can soften them back up by microwaving them in 5-10 second increments until soft.