Preheat oven to 350°F (175°C) and line a 12-cup muffin tin with paper liners.
In a large bowl, whisk together the flour, brown sugar, baking soda, cinnamon, and salt.
Stir in the grated carrots, grated apple, coconut, raisins, and walnuts until evenly distributed.
In a separate medium bowl, whisk the eggs, vegetable oil, and vanilla extract until well combined.
Pour the wet ingredients into the dry ingredients and stir until just combined; do not overmix.
Divide the batter evenly among the prepared muffin cups, filling each to the top.
Bake for 20 to 25 minutes or until a toothpick inserted into the center comes out clean.
Cool in the tin for 5 minutes before transferring to a wire rack to cool completely.