Preheat oven to 350°F. Grease a 12-cup muffin tin or line with muffin liners.
In a large bowl, whisk together the whole wheat flour, oat flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
In a medium bowl, whisk together the melted vegan butter or coconut oil, honey, flax eggs, and applesauce until combined.
Add the wet ingredients to the dry ingredients and stir until just combined. Fold in the diced apples.
Divide the batter evenly among the muffin cups. Bake for 25 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Let the muffins cool in the tin for 5 minutes before transferring to a wire rack to cool completely.