Spray a 9-inch pie pan with nonstick cooking spray. Combine the apples and caramel in a medium bowl and toss to coat.
For the batter, sift the flour, baking powder and salt into another medium bowl; whisk together and set aside.
Beat the eggs in a large bowl with an electric mixer for 1 minute on high speed, until light and frothy. Add the sugar slowly, mixing on high speed, until the eggs are very pale and light, about 4 minutes. Mix in the vanilla on low speed. Add a third of the dry ingredients at a time then mix on low speed after each addition just until smooth. Pour the batter evenly into the prepared pie pan, top with the apple-caramel mixture, and bake until golden brown and pulling away from the edges, 30 to 35 minutes.
Remove from the oven and let cool slightly on a wire rack before serving.