Preheat your oven to 375°F (190°C). Line a muffin tin with paper liners.
In a large bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
In another bowl, mix the melted butter and sugar until well combined. Add the eggs and vanilla extract, and mix well.
Gradually add the dry ingredients to the wet ingredients, alternating with the milk. Mix until just combined.
Fold in the chopped apples.
Divide the batter evenly among the muffin cups.
Bake for 20-25 minutes, or until a toothpick inserted into the center comes out clean.
Let the muffins cool in the tin for 5 minutes, then transfer to a wire rack to cool completely.