In a large bowl stir together 2 ½ cups all-purpose flour, 1 tablespoon ground cinnamon, 1 teaspoon ginger, ¼ teaspoon nutmeg, 1 teaspoon baking soda, 1 teaspoon baking powder, and 1 teaspoon salt.
In a medium-sized bowl,whisk together 1 cup vegetable oil, 1 cup light brown sugar, ½ cup granulated sugar, 4 eggs, ½ cup applesauce, and 2 teaspoons vanilla extract.
Add to the flour mixture to the oil mixture and stir to combine.
Fold in 3 cups grated carrots and ½ cup chopped pecans.
Divide the batter evenly into the prepared pans. Bake for 25-30 minutes or until golden brown and a toothpick inserted I the middle comes out clean. Let the cakes cool before frosting.
Cream Cheese Frosting
In a large bowl add 2 (8-ounce) packages cream cheese, 1 cup unsalted butter, and1 teaspoon vanilla extract. Using an electric hand mixer, mix until creamy and combined.
Add 4 cups powdered sugar 1 cup at a time until you reach the desired consistency.