Preheat the oven to 375°F (190°C). Line a 12-cup muffin tin with paper liners or grease the cups lightly.
In a large bowl, whisk together the flour, granulated sugar, brown sugar, baking powder, baking soda, salt, and ground cinnamon.
In a separate medium bowl, whisk the applesauce, milk, vegetable oil, egg, and vanilla extract until well combined.
Pour the wet ingredients into the dry ingredients and stir gently until just combined. Do not overmix; the batter should be slightly lumpy.
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 18 to 20 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.