2 1/2 cups unbleached all-purpose flour, plus more for pans
1 1/4 teaspoons baking powder
1 teaspoon baking soda
2 teaspoon ground cinnamon
¾ teaspoon salt
½ teaspoon ground ginger
½ teaspoon ground nutmeg
3 sticks (12 ounces) unsalted butter, room temperature, plus more for pans
1 cup packed light-brown sugar
1/2 cup granulated sugar
3 large eggs
2 teaspoons pure vanilla extract
1/2 cup water
1 pound carrots (6-7 medium carrots), peeled and shredded on a box grater or in a food processor (about 2 3/4 cups)
1 cup toasted pecans, finely chopped
1. Make the cake: Preheat oven to 350 degrees. Butter three 9-inch round cake pans. Line bottoms with parchment paper, and butter parchment. Dust with flour, tapping out excess. Whisk together flour, baking powder, baking soda, cinnamon, salt, ginger, and nutmeg.
2. Beat butter and sugars with a mixer on medium speed until pale and fluffy. Add eggs, one at a time, beating well after each addition. Beat 3 minutes. Add vanilla, water, and carrots. Beat until well combined, about 2 minutes. Reduce speed to low, and add flour mixture, then finely chopped pecans.
3. Scrape batter into prepared pans, dividing evenly. Bake, rotating pans halfway through, until golden brown and a toothpick inserted into centers comes out clean, about 30 minutes. Let cool in pans on a wire rack for 15 minutes. Run a knife around edges of cakes to loosen, and turn out cakes onto rack. Turn right side up, and let cool completely.
4. Place one trimmed cake on a serving platter. Spread 1 cup frosting over cake. Top with cake spread 1 cup frosting over cake. Top with remaining cake. Spread remaining frosting over top and sides. Refrigerate 1 hour (or up to 1 day, covered) before serving.