1 Prepare the pan. Preheat the oven to 350°F. Lightly grease a 9-inch springform pan and place it on a large baking sheet.
2 Make the crust. Combine the graham cracker crumbs, brown sugar, cinnamon, and salt. Stir in the melted butter until evenly moistened. Firmly press into the bottom and about 1 inch up the sides of the springform pan. Bake for 8–10 minutes, then set aside to cool slightly and reduce the oven to 325°F.
3 Make the apple filling. Melt the butter in a skillet over medium heat. Add the apples, brown sugar, cinnamon, nutmeg, salt, and lemon juice. Cook for 5–7 minutes, until slightly softened but still holding their shape. Whisk together the cornstarch and water, stir into the apples, and cook for 30–60 seconds, until thickened. Remove from the heat, stir in the vanilla, and cool completely.
4 Make the crumb topping. Combine the flour, brown sugar, cinnamon, and salt. Stir in the melted butter and vanilla until moist crumbs form. Use your fingers to press some of the mixture into larger crumb clusters. Set aside.
5 Make the cheesecake filling. Beat the softened cream cheese and sugar on medium-low speed for about 2 minutes, until completely smooth. Mix in the sour cream, vanilla, and salt. Add the eggs one at a time, mixing on low just until incorporated. Avoid overmixing once the eggs are added.
6 Assemble. Pour the cheesecake filling over the crust. Spoon the cooled apples evenly over the top, leaving behind any excess thin liquid. Scatter the crumb topping over the apples, keeping some larger clusters intact.
7 Bake. Bake at 325°F for 60–75 minutes, until the outer 2–3 inches are set and the center still has a slight jiggle. It should wobble together rather than look wet or liquid.
8 Cool. Turn off the oven, crack the door, and leave the cheesecake inside for 30 minutes. Remove and cool at room temperature for about 1 hour, or until no longer warm.
9 Chill. Cover and refrigerate for at least 6 hours, preferably overnight. Keep the cheesecake in the springform pan until completely chilled and set.
10 Slice and serve. Run a thin knife around the edge before releasing the springform pan. Slice with a sharp knife, wiping it clean between cuts. Serve chilled or let individual slices sit at room temperature for 15–20 minutes for a creamier texture.
