Preheat oven to 325°F. Lightly grease three 9-inch-diameter cake pans with 1 ½-inch-high sides. Line bottom of pans with parchment paper or coat with flour.

 Using a hand mixer, beat both sugars and vegetable oil in bowl until combined. Add eggs one at a time, beating well after each. Sift flour, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg into sugar and oil mixture. Stir in carrots.

Pour batter into prepared pans, dividing equally. Bake until toothpick inserted into center comes out clean and cakes begin to pull away from sides of pans, about 45 minutes. Cool in pans on racks 15 minutes. Turn out cakes onto racks and cool completely.

Using a mixer, beat all frosting ingredients in medium bowl until smooth and creamy.

Place 1 cake layer on platter. Top with 4 to 4-½ ice cream scoops of frosting. Spread evenly over the cake using an offset spatula, taking it over the edge. Repeat with each layer, making swirls on the top of the cake. Use offset spatula to smooth the excess frosting over the sides until you have your desired naked or semi-naked cake. 

Decorate as desired.