Prep your pan and oven. Heat the oven to 350°F (175°C).
Line a 9x9-inch baking pan with parchment, leaving overhang on two sides for easy lifting. Lightly grease the sides.
Make the crust. In a bowl, mix graham crumbs, melted butter, sugar, and a pinch of salt until it looks like wet sand. Press firmly into the pan in an even layer.
Bake for 8–10 minutes until set and lightly golden. Set aside to cool slightly.
Stir together the apples. In a medium bowl, toss diced apples with brown sugar, granulated sugar, cinnamon, nutmeg, lemon juice, and cornstarch if using. Let them sit for a few minutes to release juices.
Beat the cheesecake filling. Using a mixer, beat cream cheese and sugar on medium speed until smooth and fluffy, about 2 minutes.
Add eggs one at a time, mixing just until combined. Mix in vanilla, sour cream, and a pinch of salt. Do not overmix.
Make the streusel. In a bowl, combine flour, oats, brown sugar, cinnamon, and salt.
Cut in the cold butter with a fork or your fingers until large crumbs form and no big butter chunks remain.
Assemble the layers. Pour the cheesecake batter over the warm crust and smooth the top. Evenly scatter the apple mixture over the cheesecake, leaving any excess liquid behind if it looks watery. Sprinkle the streusel over the apples, covering most of the surface.
Bake. Bake at 350°F (175°C) for 40–45 minutes, until the center is mostly set with a slight jiggle and the topping is golden.
If the topping browns too quickly, tent loosely with foil for the last 10 minutes.
Cool completely. Set the pan on a rack and cool to room temperature. Then cover and chill for at least 3 hours, preferably overnight, to set cleanly.
Slice and serve. Use the parchment overhang to lift the slab out. Cut into 16 bars with a sharp knife, wiping between cuts.
Drizzle with caramel and a pinch of flaky salt if you like.