2 3/4 cups unbleached all-purpose flour, sifted
2 teaspoons baking powder
2 teaspoons baking soda
2 teaspoons ground cinnamon
1 1/4 teaspoon salt
1/2 teaspoon freshly grated nutmeg
1 1/2 pounds carrots (8 to 10 medium), peeled and finely shredded on a box grater or with a food processor (about 3 cups)
2 1/2 cups finely chopped walnuts or pecans (1 1/4 cup finely chopped for batter, 1 1/4 cup coarsely chopped for decorating sides of cake), optional
1 1/4 cup shredded unsweetened coconut
1/3 cup whiskey
1 1/4 cup packed light brown sugar
1/3 cup granulated sugar
1 1/4 cup olive oil plus more for greasing the pans
5 large eggs, at room temperature, beaten

Cream Cheese Frosting:
16 ounces cream cheese, at room temperature
1 tablespoon lemon juice
1 cup (2 sticks) unsalted butter, at room temperature
1 1/2 pounds powdered sugar
A few drops natural food-dye, optional