Set oven rack to the middle, and preheat oven to 350 degrees F.

In a small bowl, mix 1/4 cup of sugar with 2 teaspoons of cinnamon. Set aside.

In a medium bowl, combine flour, baking powder, and salt with a whisk. Set aside. (You can measure out the flour and salt the day before, and then add baking powder and whisk together just before using.)

Spray an 8-inch springform pan with cooking spray.

Beat 1 1/2 cups sugar, cream cheese, butter, and vanilla, at medium speed of a stand mixer, fitted with the paddle attachment, (or hand mixer) until well blended, about 4 minutes. Scrape the sides and bottom of the bowl with a silicone spatula.

Meanwhile, prepare the apples: Peel and chop the apples into 1/2-inch cubes, to make 3 cups. (See notes for an easier way to core and chop apples). Mix the apples with 3 tablespoons of the cinnamon-sugar mixture.

With the mixer on medium speed, add eggs, one at a time, to the batter, (crack into a separate bowl first to make sure you don't get shells), beating well after each addition. Scrape the sides and bottom of the bowl again.

With the mixer on low speed, pour in the flour mixture, and mix just until blended.

Gently stir the apples into the batter with your spatula until evenly distributed through the batter.

Pour the batter into the prepared pan, and smooth out the top with your spatula; sprinkle with remaining cinnamon-sugar.

Bake for 55 minutes to 1 hour and 10 minutes, or until a wooden toothpick or cake-tester inserted near the center comes out clean, and the cake pulls away slightly from the sides of the pan. (If you're using an 8 1/2 or 9-inch pan reduce the total baking time to about 50 minutes.)

Rotate the pan after 45 - 50 minutes (or less if using a larger pan); if browning too fast, cover loosely with foil.

Put the springform pan on a wire rack; cool completely before unmolding.

Unmold the cake: Run a thin knife or small offset spatula around the edges to separate the cake from the pan. Open the latch. Lift off the top part of the pan.

Set a wire rack on top of the cake and flip the cake over, onto the wire rack. Carefully remove the bottom of the pan from the cake. Re-invert the cake onto another wire rack, lightly sprayed with vegetable cooking spray. Use a large spatula to transfer the cake to a serving plate. (A dome will keep the cake fresh.)