Preheat the oven to 350˚F. Lightly grease a 9 inch springform pan with butter and set aside.
In a medium bowl, cream together ½ cup butter and sugar until light and fluffy. Add the eggs and vanilla and mix well.
In a large bowl, combine the flour, baking powder, baking soda and salt. Slowly add the wet ingredients and the sour cream until fully incorporated. Fold in apples.
For the topping, mix together the 2 ½ teaspoons of melted butter with the brown sugar and cinnamon.
Pour batter into the prepared springform pan, sprinkle the topping on top, and bake in the preheated oven for around 45-50 minutes, or until a toothpick inserted comes out clean