Preheat oven to 350F and grease an 8x8 inch pan. Combine the butter and sugars for the cake and mix until fluffy. Add the egg, oil, and vanilla and mix until combined.
Stir together the flour, baking soda, baking powder, salt, and cinnamon and stir into the butter mixture, mixing until just combined. Stir in the chopped apples. Spread into the prepared pan.
Mix together the cream cheese, sugar, and vanilla for the cream cheese layer and spread over the cake batter in the pan.
Combine the streusel ingredients using your hands or a pastry blender until well combined. Sprinkle over the cream cheese mixture.
Bake for about 45 minutes or until the topping is browned. Cool and serve.