Preheat oven to 350 degrees F (175 degrees C). Spray an 8-inch springform pan with cooking spray.
Beat 1 1/2 cup of sugar with the butter, vanilla extract, and cream cheese in a bowl until soft and creamy; beat in the eggs one at a time, beating well after each addition. Whisk together the flour, baking powder, and salt in a bowl. In a separate small bowl, stir together the cinnamon with 1/4 cup of sugar. Stir 2 tablespoons of the cinnamon-sugar mixture into the flour mixture; reserve the rest of the cinnamon sugar. Stir the flour mixture into the butter mixture to make a smooth batter, and mix in the apples. Pour batter into the prepared pan. Sprinkle the top of the batter with the reserved cinnamon-sugar mixture.
Bake in the preheated oven until the cake pulls away slightly from the edges of the pan, about 1 hour and 15 minutes. Cool cake completely on a wire rack before removing the pan and slicing the cake.