Preheat oven to 350°F. Lightly grease a 10x15 inch jelly roll pan or line with parchment paper. Set aside. Add unsweetened applesauce, granulated sugar and eggs to a large mixing bowl. Whisk to combine.
1¼ cups unsweetened applesauce, 2 cups granulated sugar, 3 large eggs
Stir in the all-purpose flour, baking soda, baking powder, salt and ground cinnamon just until combined.
2 cups all-purpose flour, 1 teaspoon baking soda, 1 ½ teaspoons baking powder, ½ teaspoon fine sea salt, 1 teaspoon ground cinnamon
Add carrots, coconut, nuts, vanilla extract and pineapple and stir just until evenly combined.
2 cups grated carrots, 1 cup shredded sweetened coconut, 1 cup chopped nuts, 1 teaspoon vanilla extract, 1 cup crushed pineapple
Transfer batter to the prepared pan, smooth top and bake for 25-30 minutes or until a toothpick comes out clean. Let cool completely before frosting.