Preheat the oven to 325°F. Line the base of a deep 9-inch springform pan and lightly grease the sides. Wrap the outside of the pan tightly with two layers of foil.
In a large pan over medium heat, melt the butter. Add the sliced apples, cider, brown sugar, and spices. Cook for about 8 minutes, stirring occasionally, until the apples are softened but still holding their shape.
In a small bowl, mix the cornstarch with the water, then stir it into the apples. Cook for a further 1–2 minutes until the mixture becomes thick, glossy, and jam-like with no loose liquid remaining.
Remove from the heat and stir in the lemon juice. Set aside to cool completely. If the mixture thickens too quickly or appears slightly separated after adding the slurry, add 1–2 tablespoons of water and gently warm over low heat, stirring until smooth and cohesive again.
Blitz the Biscoff cookies into fine crumbs and mix with the melted butter until evenly coated.
Press firmly into the base of the prepared pan, bringing the crumbs slightly up the sides.
Bake for 8 minutes, then allow to cool completely.
In the large mixing bowl of a stand mixer fitted with the paddle attachment, beat the cream cheese and sugar together until completely smooth, scraping the bowl thoroughly to ensure no lumps remain.
Add the flour, sour cream, vanilla, and spices, mixing on low speed until fully incorporated.
In a separate bowl, lightly beat the eggs, then add them in two additions, mixing on low speed just until combined. Do not over mix.
Pour half of the cheesecake batter into the cooled crust and smooth the surface.
Spoon the cooled apple filling over the batter in a thin, even layer, keeping it slightly away from the edges.
Gently pour the remaining batter over the apples and smooth the top. Tap the pan lightly on the counter to release any air bubbles.
Place the cheesecake into a pan larger than it, then put both pans inside a large roasting pan. Pour hot water around the pan until it reaches about 1 inch up the sides.
Bake for 105–120 minutes, or until the edges are set and the center has a gentle wobble. If using a thermometer, the internal temperature should be around 150ºF.
Turn the oven off, crack the door open, and leave the cheesecake inside for 1 hour.
Remove from the water bath, run a knife around the edge, and allow to cool completely at room temperature before refrigerating overnight.
In a bowl, mix the flour, oats, brown sugar, cinnamon, and salt. Rub in the cold butter until a crumbly texture forms.
Bake at 350°F for 10–12 minutes until golden. Cool completely.
In a pan, melt the butter and add the apples, sugar, cider, and spices. Cook for about 8 minutes until softened. Stir in the cornstarch slurry and cook until thickened but still slightly chunky. Allow to cool.
In a saucepan over medium heat, melt the butter and brown sugar together, stirring constantly until smooth and fully combined. Allow the mixture to gently bubble for 1–2 minutes to dissolve the sugar and develop flavor.
Reduce the heat to low and slowly add the cream, stirring continuously. Return to low–medium heat and simmer for 2–3 minutes until smooth and slightly thickened.
Remove from the heat, stir in a pinch of flaky salt, and allow to cool until pourable.
Once the cheesecake is fully chilled, spoon the apple topping over the surface, followed by the crumble. Drizzle generously with salted caramel and finish with a sprinkle of flaky sea salt if desired.