Preheat the oven to 350°F (175°C) and lightly butter a 9-inch pie dish.

In a bowl, mix graham cracker crumbs, melted butter, brown sugar, and a pinch of salt until combined. Press into the bottom and slightly up the sides of the pie dish and bake for 8-10 minutes. Let cool.

In a skillet over medium heat, melt 2 tbsp butter. Add sliced apples, brown sugar, cinnamon, nutmeg, and lemon juice. Cook until apples are just tender (5-7 minutes) and then cool to room temperature.

In a mixing bowl, beat cream cheese until smooth. Add granulated sugar and vanilla, mixing until combined. Beat in the egg, then stir in sour cream until smooth.

Spread half of the cheesecake filling over the cooled crust. Arrange cooled apple slices in a single layer on top. Spoon the remaining cheesecake filling over the apples and smooth the top.

Bake at 325°F (160°C) for 35-45 minutes until almost set. Let cool on a wire rack for 30 minutes, then refrigerate for at least 4 hours or overnight.

Before serving, warm the caramel sauce slightly, drizzle over the pie, and sprinkle with sea salt if desired.