Pre-heat the oven to 375 degrees. Grease a 12 cup muffin pan. In a medium bowl mix together flour, baking powder, baking soda, and salt. In a large bowl beat together butter, sugar, and eggs until smooth. Mix in vanilla extract. Stir in apples and then gradually blend in the flour mixture. Spoon the mixture into the prepared muffin pan.
To make the cinnamon topping- in a small bowl mix brown sugar, flour, and cinnamon. Cut in butter until the mixture is like coarse crumbs. Sprinkle over the tops of the batter in the muffin pan.
Place into the oven and bake for 20 minutes or until a toothpick comes out clean. Remove from the oven and allow to cool.