Preheat oven to 350 degrees. Spray or grease a muffin tin, or line with liners.
In a large bowl, whisk together the flour, baking soda, cinnamon, salt, and sugar. Shred carrots and apple with the shredding attachment on your food processor or a box grater. Stir the carrots, apple, nuts (if using), raisins/cranberries (if using), and coconut (if using) into the dry ingredients.
Add the oil, applesauce, and vanilla to the mixture and stir until just combined.
Divide the batter amongst your muffin cups. Bake in the middle of the oven for 20 minutes, or until they are nice and puffy and a toothpick comes out clean.
Remove the muffins from the tin after 3-5 minutes and cool completely on a cooling rack before storing in an airtight container for up to 5 days. These can also be frozen for up to 3 months. To reheat the muffins, microwave until warmed through or heat in the toaster oven.