Preheat oven to 350°F. Grease bottom and sides of a 9-inch cake pan (or a 9 to 10-inch springform pan).
In a medium bowl, sift together the flour, baking powder, baking soda and salt.
In another bowl, whisk together the sugar and oil. Add the eggs in one at a time and whisk to incorporate. Add the vanilla extract and chopped apples.
Gently and gradually fold the flour mixture into the oil mixture. Whisk to incorporate batter.
Spoon the batter into the cake pan (or spring form pan), filling about 2/3 of it. Spread the apple topping mixture on top of the cake batter, evenly covering it.
Bake in an oven anywhere from 35 minutes to 1 hour, or until a toothpick inserted in the center comes out clean. Cool completely before serving. Sprinkle with powdered sugar, if preferred.