1. Preheat oven to 325°F (163°C). Grease a 9-inch springform pan and wrap the outside with foil to prevent leaks.

2. In a bowl, combine graham cracker crumbs, granulated sugar, and melted butter. Press evenly into the bottom of the pan.

3. Beat cream cheese until smooth. Add sugar and mix until combined. Add eggs one at a time, beating after each addition. Mix in vanilla extract. Pour over the crust.

4. In a skillet, cook sliced apples with butter, brown sugar, and cinnamon over medium heat until just tender. Cool slightly, then layer over cheesecake filling.

5. In a bowl, mix oats, flour, brown sugar, cinnamon, and cold butter. Blend with fingers or a fork until crumbly. Sprinkle evenly over apples.

6. Bake for 60-70 minutes, or until the cheesecake is set at the edges and just slightly wobbly in the center. Tent with foil if topping browns too quickly.

7. Remove from oven and cool completely. Chill in refrigerator at least 6 hours or overnight for best results.

8. Release from pan, slice, and drizzle each piece with caramel sauce before serving.