Preheat oven to 350F. Line a muffin tin with papers and set aside.
In a medium size bowl, combine the buckwheat flour, almond flour, arrowroot flour, baking powder and sea salt.
In a separate bowl, combine the banana, eggs, butter, honey and vanilla.
Combine the dry ingredients with the wet ingredients.
Fold in the apple, coconut flakes, carrots, and walnuts (saving some to add to the tops of the muffins before putting into the oven).
Fill each paper liner about 3/4 full, and top with some of the remaining apple, coconut flakes, carrots and walnuts.
Bake for 17-20 minutes, or until the center is set.
Remove from the oven and let cool for 10 minutes before transferring to a wire rack to cool completely.
Store in a container for up to 5 days at room temperature.