3/4 cup (1 1/2 sticks) unsalted butter, room temperature
3 (8-ounces each) cream cheese, room temperature
3 cups confectioners' sugar
1 tablespoon freshly grated orange zest
2 tablespoons freshly grated ginger
Pinch of salt
How to make it
Heat oven to 375 degrees. Butter two 8-by-2-inch round cake pans. Dust pans with flour, and tap out any excess. Set pans aside. Spread pecans in a single layer on an ungreased baking pan, and toast in the oven until lightly golden, about 7 minutes. Remove pan from oven, and let stand until completely cool. Reduce temperature to 300 degrees. Finely chop pecans, and set aside.
Using the smallest holes (less than 1/4 inch in diameter) of a box grater, grate carrots, yielding 2 1/2 cups. Place carrots, eggs, buttermilk, vanilla, sugar, vegetable oil, and ginger in a large bowl; whisk until well combined.
In a medium bowl, whisk together flour, baking powder, baking soda, salt, and cinnamon. Using a rubber spatula, fold the flour mixture into the carrot mixture until combined. Fold in the toasted pecans.
Divide batter between the two cake pans, and bake until a cake tester inserted into the middles comes out clean, about 1 hour. Remove pans from oven, and transfer to a wire rack to cool, 15 minutes. Turn cakes out onto rack; let stand until completely cool.
Using a serrated knife, trim tops of the cakes so surfaces are level. Slice each layer in half horizontally. Place a layer on a cake stand or cardboard round, and spread 3/4 cup frosting over top. Place a second cake layer on top, and spread with another 3/4 cup frosting. Repeat with third layer and another 3/4 cup frosting. Place last cake layer on top, and spread the remaining frosting over the top and the sides of the assembled cake. Transfer to refrigerator, and chill 3 to 4 hours.
Cream Cheese Frosting:
Place butter in the bowl of an electric mixer fitted with the paddle attachment, and beat on medium-high speed until fluffy, about 2 minutes. Add cream cheese, and beat until well combined and fluffy, about 2 minutes more. Add the remaining ingredients, and beat 5 minutes more. Use immediately, or store in the refrigerator in an airtight container for up to two days.