In a food processor, pulse the Biscoff cookies into fine crumbs. Add melted butter, then process until the mixture resembles wet sand. Press firmly into the bottom and sides of a 9-inch (23cm) springform pan, using the back of a spoon or a glass.
Bake the crust: Bake for 8–10 minutes, then set aside to cool slightly.
Make the cheesecake filling: In a large bowl, using a hand or stand mixer, beat the cream cheese and sugar until completely smooth, about 2 minutes. Add the sour cream, vanilla bean paste, cinnamon (if using), nutmeg (if using), and a pinch of salt. Mix until combined. Add the eggs one at a time, mixing just until incorporated after each addition. Do not overmix. Add the cornstarch and mix just until incorporated.
Prepare the crumble: In a medium bowl, whisk together the flour, oats, light brown sugar, cinnamon, and salt. Work the cold, cubed butter into the dry ingredients using your fingers or a pastry blender until coarse crumbs form with some pea-sized chunks. Avoid overmixing, the crumble should remain coarse with visible butter pieces. . Keep the crumble chilled in the refrigerator until needed for the topping.
Make the apple topping: In a large skillet, combine the brown sugar, cornstarch, cinnamon, and salt. Add the sliced apples and toss until evenly coated. Add the butter and lemon juice, then cook over medium heat for 5–7 minutes, stirring occasionally, until the apples begin to soften and the juices have thickened into a glossy sauce. Be careful not to overcook the apples, they should still hold their shape. Remove from the heat and let cool completely before using.
Assembly: Pour the cheesecake batter over the cooled crust. Spoon the cooled apple topping evenly over the batter, distributing it gently without pressing it down. Sprinkle the crumble topping evenly over the apples.
Bake the cheesecake: Bake at 325°F (160°C) for 55–70 minutes, or until the edges are set and the center still has a slight jiggle. Don't overbake.
Turn off the oven and leave the cheesecake inside with the door closed for 1 hour. Remove and cool at room temperature for another hour, then refrigerate for at least 4 hours, preferably overnight.
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Notes
Biscoff cookie crust: You can use any biscuits or crackers you like. I chose Biscoff because they add warm caramel-spice notes and pair well with apple desserts. You can also use digestive biscuits, gingersnaps, petit beurre, or shortbread.
Apples: For the best flavor and texture, use firm baking apples that hold their shape during cooking. Granny Smith is my favorite because its tartness perfectly balances the rich cheesecake and sweet crumble. Honeycrisp, Pink Lady, Braeburn, or Jonagold also work well. Slice the apples into ¼-inch (6mm) thick slices. Thinner slices may become too soft, while thicker slices can stay slightly firm after baking.
Baking times: Baking time may vary depending on your oven and the type of pan you use. The cheesecake is ready when the edges look set but the center still jiggles slightly when gently shaken.
Prevent the apples from sinking: The apple topping should be completely cooled before assembling the cheesecake. Spoon the apples gently over the batter and avoid pressing them down. The thick cheesecake batter will support the topping as it bakes, helping keep the apples and crumble beautifully layered on top.
Storage: Store the cheesecake covered in the refrigerator for up to 5 days.