Preheat oven to 350°F (175°C) and grease a 12-cup muffin tin or line with paper liners.
In a large bowl, whisk together the whole wheat flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
In a separate medium bowl, whisk together the applesauce, maple syrup, melted coconut oil, egg, and vanilla extract until well combined.
Pour the wet ingredients into the dry ingredients and stir with a spatula until just combined. Do not overmix.
Divide the batter evenly among the 12 muffin cups.
Bake for 18 to 22 minutes, or until a toothpick inserted into the center comes out clean.
Let the muffins cool in the pan for 5 minutes before transferring to a wire rack to cool completely.