Preheat the oven to 350°F (175°C). Line a 12-cup muffin tin with paper liners or grease the cups.
In a medium bowl, whisk together the gluten free flour blend, baking powder, baking soda, salt, ground cinnamon, and ground nutmeg until well combined.
In a large bowl, beat the eggs with granulated sugar and brown sugar until the mixture is light and fluffy, about 2 minutes.
Add the applesauce, vegetable oil, and vanilla extract to the egg and sugar mixture. Stir until combined.
Gradually add the dry ingredients to the wet ingredients, stirring gently until just combined. Do not overmix.
Fold in the chopped apples evenly into 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 tin for 5 minutes.
Transfer the muffins to a wire rack to cool completely before serving.