Preheat the oven to 375°F. Grease or line a 12-cup muffin tin with paper liners.
In a large bowl, whisk together the 2 cups flour, the sugar, baking powder, salt, and cinnamon. In a separate bowl, coat the apples with 1 tablespoon of flour.
In another bowl, whisk together the butter, applesauce, egg, milk, and vanilla extract.
Add the wet ingredients to the dry ingredients and mix until just combined.
Fold in the coated apples until evenly distributed.
Spoon the batter into the prepared muffin tin, filling each cup about 3/4 full. Sprinkle the tops of the muffins with raw sugar.
Bake in the preheated oven for 20 minutes, or until a toothpick inserted into the center of a muffin comes out clean.
Allow the muffins to cool in the pan for 5 minutes, then transfer them to a wire rack to cool completely.