Preheat your oven to 350°F (175°C). In a medium bowl, combine graham cracker crumbs, melted butter, and sugar. Press the mixture firmly into the bottom of a 9-inch springform pan to form an even layer. Bake the crust for 10 minutes, then remove and let it cool.

In a large mixing bowl, beat the cream cheese and sugar until smooth and creamy. Add the vanilla extract and mix until combined. Beat in the eggs one at a time, ensuring each is fully incorporated before adding the next. Stir in the sour cream until smooth. Gently fold in the apple slices, cinnamon, and nutmeg.

Pour the cheesecake filling over the cooled crust, spreading it evenly. Tap the pan gently to remove air bubbles. Bake for 50-60 minutes, or until the edges are set but the center still jiggles slightly. Turn off the oven, crack the oven door, and let the cheesecake cool inside for 1 hour. Refrigerate for at least 4 hours or overnight.

In a medium saucepan over medium heat, melt the sugar, stirring constantly until it turns deep amber. Carefully add the butter and whisk until fully melted. Slowly pour in the heavy cream, stirring continuously. Remove from heat and stir in the sea salt. Let cool slightly before drizzling over the cheesecake.

Once chilled, remove the cheesecake from the springform pan. Drizzle the salted caramel sauce generously over the top. Slice with a sharp knife, cleaning the blade between cuts. Serve with additional apple slices or a dollop of whipped cream if desired.