Preheat oven to 325°F (163°C). Grease a 9-inch springform pan.
In a bowl, combine graham cracker crumbs, sugar, and melted butter. Press firmly into the bottom of the prepared pan. Bake for 10 minutes and let cool slightly.
In a large mixing bowl, beat cream cheese until smooth and creamy.
Add sugar and mix until fully incorporated.
Add eggs one at a time, mixing on low speed after each addition.
Stir in vanilla extract and sour cream until just combined.
Pour cheesecake filling over the cooled crust and smooth the top.
Place the springform pan inside a larger roasting pan. Fill the roasting pan with hot water halfway up the sides of the cheesecake pan to create a water bath.
Bake for 55–65 minutes, until the center is almost set but still slightly jiggly.
Turn off the oven, crack the door open, and let the cheesecake cool inside for 1 hour.
Remove cheesecake from oven and refrigerate for at least 4 hours or overnight.
For the apple topping, melt butter in a skillet over medium heat. Add diced apples, brown sugar, cinnamon, and nutmeg. Cook until apples are soft and syrupy, about 8 minutes.
Allow apple mixture to cool to room temperature.
To prepare the salted caramel sauce, heat sugar in a saucepan over medium heat, stirring constantly until melted and amber colored.
Add butter carefully and stir until melted.
Slowly whisk in heavy cream. The mixture will bubble rapidly.
Boil for 1 minute, then remove from heat and stir in sea salt.
Let caramel cool slightly before using.
Spoon the apple pie topping over the chilled cheesecake.
Drizzle generously with salted caramel sauce before slicing and serving.