Preheat your oven to 350°F (175°C). Prepare the muffin tin by lining it with muffin liners or lightly greasing it.
In a large mixing bowl, combine the all-purpose flour, granulated sugar, baking powder, baking soda, salt, ground cinnamon, and ground nutmeg. Whisk together until evenly mixed.
In another bowl, whisk together the eggs, applesauce, milk, vegetable oil, and vanilla extract until smooth.
Pour the wet ingredients into the dry ingredients. Stir gently with a rubber spatula until just combined. Be careful not to overmix.
Fold in the diced apples until evenly distributed throughout the batter.
Divide the batter evenly among the 12 muffin cups, filling each about ⅔ full.
If desired, in a small bowl, mix together the brown sugar and cinnamon. Sprinkle this mixture over the tops of the muffins for added sweetness and flavor.
Bake in the preheated oven for 18-20 minutes or until a toothpick inserted into the center comes out clean.
Allow the muffins to cool in the pan for about 5 minutes before transferring them to a cooling rack to cool completely.
Enjoy your delicious Apple Pie Muffins warm or at room temperature!