In a bowl, combine the flour and brown sugar. Cut in the butter with a pastry blender, or a fork, until the mixture is crumbly. (You’re going for a sand type texture with coarse crumbles remaining). Press the dough evenly into a 13 × 9-inch baking pan. Bake 15 minutes or until lightly browned.
For the Cream Cheese Layer:
While the crust is baking, in a large bowl, beat the cream cheese with sugar until smooth. Add the eggs, 1 at a time, beating after each addition, stopping if needed, to scrape down the sides of the bowl. Add the vanilla and mix until combined.
Don’t over-beat the cheesecake batter, just mix until everything is blended well. Pour the cream cheese batter over the crust.
Peel, core, and chop the apples into pieces. Toss the apples with the cinnamon and sugar.
Spread the apple chunks over the cream cheese mixture.
For the topping:
In a small bowl, combine the flour, oats, and brown sugar. Cube the butter and using a pastry blender, or fork, create a crumbly mixture (once again, not smooth – crumbly) and sprinkle heavily over the cream cheese layer. You may not have to use the entire mixture – or you may – you’r call.
Bake 25 minutes at 350 degrees F. Reduce the temperature to 300 degrees F for the last 5 minutes, or until cream cheese layer is set. Cool completely and serve with caramel topping if desired.