Preheat oven to 350°.
Place 1 1/2 cups sugar, cream cheese, butter, and vanilla in a large bowl; beat with a mixer at medium speed until well blended (about 4 minutes). Add eggs, 1 at a time, beating well after each addition. Lightly spoon flour into dry measuring cups; level with a knife. Combine flour, baking powder, and salt, stirring with a whisk. Add flour mixture to cream cheese mixture, beating at low speed until well blended.
Combine remaining 1/4 cup sugar and 1 teaspoon cinnamon. Combine 2 tablespoons cinnamon mixture and chopped apple in a bowl, and stir apple mixture into batter. Pour the batter into an 9-inch springform pan coated with cooking spray. Sprinkle with the remaining cinnamon mixture. Bake at 350° for 1 hour or until cake pulls away from the sides of the pan. Cool cake completely on a wire rack. Cut into 12 wedges, using a serrated knife.