Preheat oven to 350 degrees. Line cupcake pan with 12 cupcake liners. Set aside.
In a bowl fitted for a stand mixer, cream butter and sugars together until fluffy, for about 3-4 minutes. Add egg and beat until combined. Add egg yolk and vanilla and beat until combined. Add sweet potato puree and beat until fluffy again, about 1-2 minutes.
In another medium bowl, add flours, baking powder, baking soda, salt, cinnamon, and nutmeg and whisk together. Add half of flour mixture to butter mixture and mix until combined. With the mixer on low, slowly pour in milk. Mix until combined. Add the rest of the flour and mix just until combined. Don't overmix!
Scoop about 1/4 cup of batter into each muffin liner. They should be about 3/4 full. Place cupcakes in preheat oven and immediately reduce temperature to 325 degrees. Bake for 18-22 minutes, or until toothpick comes out clean when inserted.
Remove cupcakes pan from oven and place pan on wire rack to cool for 5 minutes. Remove cupcakes from pan and let them finish cooling. Do not frost cupcakes until they cool completely! Frosting recipe below.