Preheat the oven to 350°F (175°C) and grease two 8-inch round cake pans or one 9x13 cake pan (or line them with parchment paper).
In a large bowl, whisk together the whole wheat flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
In another bowl, whisk together the applesauce, vegetable oil, honey/maple syrup, and eggs until smooth and combined.
Add the wet ingredients to the dry ingredients and mix until just combined.
Fold in the grated carrots, crushed pineapple, coconut (if using), and nuts (if using).
Divide the batter evenly between the prepared cake pan(s).
Bake for 25-30 minutes or until a toothpick inserted into the center comes out clean.
Cool the cakes in the pan(s) for 10 minutes, then remove them from the pan(s) and let them cool completely on a wire rack.