Preheat the oven to 350°F (175°C) and line a 12-cup muffin tin with paper liners.
In a large bowl, whisk together the gluten free flour blend, xanthan gum, baking powder, baking soda, salt, and ground cinnamon until well combined.
In a separate medium bowl, beat the eggs with the granulated sugar and brown sugar until the mixture is smooth and slightly thickened.
Add the unsweetened applesauce, whole milk, vegetable oil, and vanilla extract to the egg and sugar mixture. Stir until fully combined.
Pour the wet ingredients into the dry ingredients and gently fold together until just combined, being careful not to overmix.
Fold in the finely chopped apple pieces 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 let them cool in the tin for 5 minutes before transferring them to a wire rack to cool completely.