Coat the sides and bottom of the baking pan thoroughly with butter or non-stick spray.
Core the apples and cut them in 1/2-inch slices. In a medium saucepan over medium-low heat, melt the butter and stir in the brown sugar and corn syrup until it is well dissolved. Add the cut apples to the caramel syrup. When all of the apples are in, stir gently to make sure they are all coated. Spread the mixture in the bottom of the prepared baking pan.
Whisk together, eggs, milk and vanilla to make a custard. Arrange bread slices in a single layer over the apple mixture. Pour the egg mixture over, making sure all of the bread slices are moistened. Cover and refrigerate overnight (8-10 hours).
In the morning, take the pan out of the refrigerator and let it come closer to room temperature while the oven is preheating to 350 degrees. Uncover the pan and bake 45-60 minutes, until the custard is set. To serve, turn each serving over so that the caramel apple side is up. Sprinkle with cinnamon sugar.