Preheat the oven to 425ºF. Spray 16 muffin tins with nonstick cooking spray. Set aside.

In a large bowl, combine the eggs, granulated sugar, brown sugar, vegetable oil, applesauce, and vanilla extract. Whisk until smooth.

In another bowl, whisk together the flour, baking soda, cinnamon, and salt.

Stir the carrots and apple into the flour mixture until it is well coated.

Add the wet mixture to the flour mixture and stir until mostly combined. Add the raisins, pecans, and coconut. Mix just until combined.

Fill each muffin tin with the batter. The cups should be almost filled to the top.

Bake in the preheated oven at 425ºF for 5 minutes, then turn the heat down to 350ºF, leaving the muffins in the oven the whole time. Continue to bake until a tester inserted in the center comes out clean, about 18 more minutes. If the muffins start to get too dark on top, cover with a sheet of foil.

Once baked through, remove from the oven and let the muffins cool for about 5 minutes before removing from the baking tin.