Peel, core, and slice the apples into even pieces. Toss them with lemon juice while cutting to prevent browning.

Cook the apples with the sugar and cinnamon in a pan for 3–5 minutes until slightly softened but not fully cooked. Remove the apples and set aside.

Mix a few tablespoons of the hot apple sauce with cornstarch until smooth, then stir into the pan. Cook for about 1 minute until thickened.

Let both the apple mixture and apple sauce cool to room temperature.

Cut butter into small chunks and let it come to room temperature. Whisk together flour, salt, granulated sugar, brown sugar, and cinnamon.

Add the room temperature butter chunks to the mixture and mix just until the dry ingredients are coated.

Chill the crumble in the fridge.

Melt the butter until fully liquid, then set aside to cool slightly. Crush the graham crackers into fine crumbs.

Stir a pinch of salt and the cinnamon into the crumbs, then add melted butter and mix until wet sand texture.

Press the mixture evenly into the bottom and sides of the springform pan, then chill.

Bake the crust in a preheated 350°F (175°C) oven for 8–10 minutes, let cool completely.

Preheat the oven to 325°F (165°C) and prepare a roasting pan for the water bath larger than the springform pan.

Wrap the outside of the springform pan in aluminum foil to prevent leaks.

Place cream cheese into a stand mixer and cream on medium-low speed for 2 minutes until smooth.

Add granulated sugar and continue creaming for 2 minutes until silky.

Add sour cream, lemon juice, vanilla, and salt. Mix on low speed until combined.

Lightly whisk eggs until blended, then slowly add to the mixture, mixing until fully incorporated.

Layer the cheesecake in the prebaked crust: ½ cheesecake batter, ½ apple compote, ½ cheesecake batter, ½ apple compote, all the crumble.

Press the crumble gently on top and move to the roasting pan. Pour hot water into the roasting pan.

Bake the cheesecake in the water bath at 325°F (165°C) for 75-85 minutes, until edges are set.

Turn off the oven and leave the cheesecake inside for another 60 minutes.

Cool the cheesecake at room temperature for about 1 hour, then chill in the refrigerator for at least 6 hours.

Let the cheesecake sit at room temperature for 20-30 minutes before slicing and serve with apple caramel.