Preheat the oven to 350°F (175°C). Line a 9x13-inch baking pan with parchment, leaving overhang on the long sides for easy lifting. Lightly grease the parchment.

Make the crust: In a bowl, mix melted butter, flour, sugar, salt, and vanilla until a soft dough forms. Press evenly into the pan, packing it down firmly. Par-bake for 10–12 minutes until set but not browned. Set aside.

Prep the apples: In a bowl, toss diced apples with brown sugar, cinnamon, nutmeg, lemon juice, and cornstarch. Set aside to let the juices start releasing.

Make the cheesecake layer: Beat the cream cheese and sugar until smooth and fluffy, about 2 minutes. Add sour cream, eggs, vanilla, and a pinch of salt. Mix just until combined and silky. Do not overbeat to avoid excess air bubbles.

Make the streusel: In another bowl, whisk flour, oats, brown sugar, cinnamon, and salt. Cut in the cold butter with a pastry cutter or your fingers until it forms pea-sized crumbs. Keep it a bit chunky.

Assemble: Pour the cheesecake batter over the warm crust and spread evenly. Scatter the apple mixture across the top in an even layer. Sprinkle the streusel over the apples, covering most of the surface.

Bake: Return the pan to the oven and bake for 35–40 minutes, until the edges are set and the center jiggles slightly like Jell-O. If the streusel is browning too fast, tent loosely with foil for the last 10 minutes.

Cool completely: Place the pan on a rack and cool to room temperature, then chill for at least 3 hours (overnight is best) to set.

Finish and serve: Lift the slab out by the parchment. Drizzle generously with caramel sauce. Add a pinch of flaky sea salt if you like that sweet-salty finish. Slice into bars with a sharp knife, wiping between cuts for clean edges.