Preheat oven to 350°F (180℃). Spray a 9x13 pan with cooking spray and set aside.
In a large mixing bowl, whisk together the sugar, applesauce, oil and eggs in a large bowl. 2 cups (400 g) granulated white sugar ½ cup (120 ml) vegetable oil ½ cup (100 g) applesauce 4 large eggs
In the same bowl, add the flour, baking soda, baking powder, cinnamon, nutmeg, and ginger. Stir to combine. 2 cups (240 g) all purpose flour ½ teaspoon salt 1 teaspoon baking soda 1 teaspoon baking powder 2 teaspoons cinnamon ¼ teaspoon ground nutmeg ¼ teaspoon ground ginger
Fold in the carrots and walnuts just to combine. 3 cups (297 g) grated carrots 1 cup (128 g) walnuts
Pour into your prepared pan. Bake for 35-40 minutes or until a toothpick comes out clean. Cool completely.
In a bowl of a stand mixer with a paddle attachment, cream butter and cream cheese on medium speed until light and fluffy, about 2 minutes. 8 tablespoons (1 stick, 113 g) unsalted butter 8 ounces (228 g) cream cheese
Add powdered sugar (about 1/2 cup at a time) and beat on low speed until combined. Add vanilla and blend to combine. Spread on top of cooled cake. 4 cups (452 g) powdered sugar 2 teaspoons vanilla extract