Preheat oven to 375ºF/190ºC. Line 12 muffin cups with liner papers or grease well.
Cut up the apples into 1/2 inch cubes and place in a bowl. Set aside.
In a large bowl, sift together flour, baking powder, salt, cinnamon, and nutmeg. Add granulated sugar and brown sugar, and mix.
In a medium bowl, whisk together eggs, milk, melted butter, and vanilla extract until combined. Pour the wet ingredients into the dry ingredients and stir with a wooden spoon or rubber spatula just until combined. Do not over mix. The batter at this time should be thick and lumpy (with some ribbons of flour still throughout the batter). Fold in apples.
Evenly distribute the batter between the 12 liners, each 3/4 of the way full. All the batter should be used up. Bake for 18-20 minutes or until a toothpick inserted into the center of a muffin comes out clean. Remove from the oven. Allow to cool for 10 minutes in the pan before transferring to a wire rack to cool completely.
Muffins are best the same day they are made, but can be stored in an airtight container at room temperature for 2-3 days. Muffins can also be frozen for up to 2 months.