Preheat oven to 375°F (190°C). Grease a 12-cup muffin tin or line with paper liners.
In a medium bowl, whisk together flour, baking powder, baking soda, salt, and cinnamon.
In a large bowl, beat together butter, white sugar, and brown sugar until light and fluffy. Add eggs one at a time, beating well after each addition. Stir in vanilla extract.
Gradually add the flour mixture to the butter mixture, mixing just until combined. Fold in grated apples.
Divide batter evenly among the prepared muffin cups.
In a small bowl, combine brown sugar, flour, and cinnamon for the topping. Cut in butter until mixture resembles coarse crumbs. Sprinkle topping evenly over muffin batter.
Bake in preheated oven for 20 minutes, or until a toothpick inserted into the center of a muffin comes out clean. Cool in the pan for 5 minutes, then transfer to a wire rack to cool completely.