Preheat the oven to 350°F (175°C). Line a muffin tin with 8 paper liners or grease the muffin cups.
Place the rolled oats in a blender or food processor and blend until they reach a fine flour-like consistency.
In a large bowl, combine the oat flour, baking powder, baking soda, ground cinnamon, ground nutmeg, and salt. Mix well.
In a separate bowl, whisk the eggs, unsweetened applesauce, honey, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients and stir until just combined.
Fold in the finely chopped apple pieces gently.
Divide the batter evenly among the prepared muffin cups.
Bake in the preheated oven 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 allow them to cool in the tin for 5 minutes.
Transfer the muffins to a wire rack to cool completely before serving.