Preheat oven to 350 degrees F (180 degrees C). Grease a 9×9 square baking pan.
Cream Egg (2) and Granulated Sugar (3/4 cup) in the bowl of a stand mixer. Add Unsalted Butter (8 tablespoon) one at a time and mix until fully incorporated into the butter mixture.
Mix in Vanilla Extract (1 teaspoon).
In a separate bowl, combine All-Purpose Flour (1 1/4 cup), Baking Powder (1 1/2 teaspoon), Salt (1/4 teaspoon), Ground Cinnamon (1 teaspoon), and Ground Nutmeg (1 pinch). Mix to combine.
Alternately add the flour mixture and the Sweet Potato Purée (3/4 cup) into the creamed mixture until a stiff batter is formed.
Spread batter into the prepared pan.
Bake for 25 minutes.
While it bakes, make the frosting. Combine Powdered Confectioners Sugar (2 cup), Unsalted Butter (2 tablespoon), and Maple Syrup (3 tablespoon) in the bowl of a stand mixer. Add more or less maple syrup and confectioners sugar as needed.
Let the cake cool completely before frosting. Enjoy!