Preheat oven to 350℉ and prepare a muffin tin with paper liners or grease each muffin cup.
In a large bowl, whisk the eggs, canola oil and vanilla extract until well combined. To this, add the grated carrot and apple.
In a separate bowl, combine the flour, sugar, baking soda, baking powder, ground cinnamon and salt.
Gently fold the dry ingredients into the wet ingredients and stir until just combined. Add the walnuts and coconut (if using) and stir.
Evenly divide the batter among the 12 muffin tins. Bake the muffins for 20-23 minutes, or until an inserted toothpick comes out clean.
Let the muffins cool for 5-10 minutes before enjoying. The muffins will keep well in the fridge for roughly 5 days and in the freezer for 3 months.