- Preheat oven to 350 degrees.
- For the crust: Pulse flour, graham cracker, and brown sugar in food processor. Add cubed, cold butter and pulse until crumbly. Press in bottom of a 9×12-inch sheet pan with low sides. Bake 10 minutes; cool.
- For the apple filling: Cook apples in pan with the butter until softened. Add sugar and spice and cook until caramelized. Stir in heavy cream. Layer apples on top of baked crust.
- For the cream cheese filling: In a mixer, cream together cream cheese and brown sugar until fluffy. Add eggs one at a time, combining after each addition. Mix in sour cream and vanilla. Pour mixture over the apples and baked crust. Bake for 40 minutes.
- For the streusel: Pulse brown sugar, flour, and nuts in the food processor. Add cubes of cold butter and pulse until crumbly. Spread on sheet tray and bake until brown. Cool and crumble with hands. Reserve for assembly.
- For the caramel sauce: Combine sugar, water, and lemon juice in a small saucepan and cook over medium heat until caramelized, being careful not to let mixture crystallize. Remove from heat. Carefully whisk in cream. Caramel will bubble up quite a bit when cream is added.
- To assemble: Finish cheesecake by sprinkling on streusel. Cut cheesecake into 10 pieces and place on small plates. Pour on caramel sauce just before serving