Preheat the oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners or grease with coconut oil.
In a large bowl, whisk together the almond flour, baking soda, salt, ground cinnamon, and ground nutmeg until well combined.
In a separate bowl, beat the eggs. Add honey, unsweetened applesauce, melted coconut oil, and vanilla extract. Mix until smooth.
Pour the wet ingredients into the dry ingredients and stir until just combined.
Fold in the finely chopped apple pieces gently into the batter.
Divide the batter evenly among the 12 muffin cups, filling each about 3/4 full.
Bake for 22 to 25 minutes or until a toothpick inserted into the center of a muffin comes out clean.
Remove the muffins from the oven and let them cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.