Preheat the oven to 350°F. Lightly grease your baking pan or pans. For easier removal, line the bottoms with parchment paper or use a nonstick baking spray that contains flour.

In a large bowl, combine the applesauce, sugar, and eggs. Mix well.

In a separate bowl, combine the flour, baking soda, baking powder, salt, and cinnamon.

Gradually add the dry ingredients to the wet ingredients, stirring until just combined.

Stir in the grated carrots, shredded coconut, chopped nuts if using, vanilla, and pineapple. Mix until evenly incorporated.

Pour the batter into a lightly greased 9 × 13-inch pan, two 9-inch round pans, or three 8-inch round pans. Spread the batter evenly.

Bake according to the pan size:

9 × 13-inch or two 9-inch pans: 35–40 minutes

Three 8-inch pans: 25–30 minutes

The cake is done when a toothpick inserted into the center comes out clean or with a few moist crumbs.

Allow the cakes to cool in the pans for about 10 minutes. Remove them from the pans and transfer to a cooling rack. Let cool completely before frosting.

Cream Cheese Frosting

Beat the softened butter and cream cheese together until light and fluffy.

Add the vanilla and powdered sugar. Beat until smooth and creamy.

Gradually add the reserved pineapple juice, beating until the frosting reaches your desired consistency. If the frosting becomes too thin, add a little more powdered sugar.

Once the cake is completely cool, frost as desired. For layered cakes, place one cake layer on a cake plate or stand, spread with frosting, and continue layering and frosting the remaining cakes.

If desired, sprinkle the finished cake with chopped pecans or coconut.

Refrigerate for about 1 hour before serving for best results.