Preheat your oven to 350°F (175°C). Line a muffin tin with paper liners or grease the cups with cooking spray.
In a large mixing bowl, combine the all-purpose flour, granulated sugar, baking soda, ground cinnamon, and salt. Stir until well combined.
In a separate bowl, whisk together the eggs, vegetable oil or melted coconut oil, unsweetened applesauce, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and stir until just combined. Be careful not to overmix.
Fold in the grated carrots, shredded coconut, chopped nuts, crushed pineapple, and raisins or dried cranberries until evenly distributed throughout the batter.
Spoon the batter into the prepared muffin tin, filling each cup about 3/4 full.
Bake in the preheated oven for 20 to 25 minutes, or until the muffins are golden brown and a toothpick inserted into the center comes out clean.
Remove the muffins from the oven and let them cool in the tin for a few minutes before transferring them to a wire rack to cool completely.