Preheat the oven to 350°F (175°C) and line a 12-cup muffin tin with paper liners or grease the cups.
In a large bowl, whisk together the gluten free all-purpose flour, baking powder, baking soda, salt, ground cinnamon, and ground nutmeg until well combined.
In a separate medium bowl, whisk the granulated sugar, light brown sugar, eggs, unsweetened applesauce, vegetable oil, and vanilla extract until smooth.
Add the wet ingredients to the dry ingredients and stir gently until just combined.
Fold in the chopped apple and milk until evenly distributed. Do not overmix.
Divide the batter evenly among the 12 muffin cups, filling each about 3/4 full.
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 pan for 5 minutes.
Transfer the muffins to a wire rack to cool completely before serving.