Preheat the oven to 400 degrees F and coat a 6-cup donut pan with nonstick spray.
Add the egg, milk, butter, sweet potato, and vanilla to a medium bowl. Stir well to combine.
Stir in the rest of the ingredients and spoon into prepared donut pan, filling each full. (You'll use a heaping ¼ cup batter in each.)
Bake for 16-18 minutes or until lightly golden brown around the edges and a cake tester inserted into the center comes out clean.
Remove from oven, let sit for 2-3 minutes, then invert onto a wire rack to cool slightly.
Serve topped with a drizzle of frosting (see below in the Notes), if desired.
