Preheat the oven to 350°F (175°C). 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, and eggs until smooth and slightly fluffy.
Add the unsweetened applesauce, whole milk, vegetable oil, and vanilla extract to the sugar and egg mixture. Whisk until fully combined.
Pour the wet ingredients into the dry ingredients and gently fold together with a spatula until just combined. Do not overmix.
Fold in the diced apples evenly throughout the batter.
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.