Preheat the oven to 350 degrees F (175 degrees C). Coat an 8-inch springform pan with cooking spray.

Beat 1 1/2 cups sugar, cream cheese, butter, and vanilla extract together in a bowl with an electric mixer until soft and creamy; beat in eggs, one at a time, beating well after each addition.

Whisk flour, baking powder, and salt together in a bowl. Combine 1/4 cup sugar and cinnamon in a separate small bowl. Stir 2 tablespoons cinnamon-sugar into flour mixture; reserve remaining cinnamon-sugar mixture.

Stir flour mixture into cream cheese mixture until batter is smooth; stir in apples. Pour batter into the prepared pan. Sprinkle batter with reserved cinnamon-sugar mixture.

Bake in the preheated oven until cake slightly pulls away from edges of the pan, about 1 1/4 hours. Cool cake completely on a wire rack before removing from the pan and slicing.