1. Preheat your oven to 325°F (165°C) and line a 9×13-inch baking pan with parchment paper.
2. Combine graham cracker crumbs, melted butter, and granulated sugar in a bowl for the crust.
3. Press the mixture into the prepared pan to form an even layer and bake the crust for 10 minutes. Let it cool slightly.
4. In a mixing bowl, beat cream cheese and sugar together until smooth and creamy.
5. Add sour cream and vanilla extract to the cream cheese mixture, blending well.
6. Mix in eggs one at a time on low speed to avoid overmixing.
7. Pour the cheesecake filling over the pre-baked crust, spreading it evenly.
8. In a skillet, sauté sliced apples with butter, brown sugar, lemon juice, and cinnamon until tender and caramelized.
9. Let the cooked apples cool briefly before layering them on top of the cheesecake filling.
10. Prepare the streusel topping by combining flour, oats, brown sugar, and cold cubed butter. Mix until crumbly.
11. Sprinkle the streusel topping evenly over the apple layer.
12. Bake the assembled cheesecake at 350°F (175°C) for 45–55 minutes, covering with foil if needed to prevent over-browning.
13. After baking, allow the cheesecake to cool gradually in the oven with the door slightly open, then refrigerate for at least 4 hours or overnight.
14. Make the caramel sauce by caramelizing sugar and water in a saucepan. Stir in heavy cream, butter, and vanilla extract, then let it cool.
15. Slice the chilled cheesecake into bars for serving.
16. Drizzle caramel sauce over each bar before serving, and optionally garnish with whipped cream or apple slices.