Step 1: Prepare the CrustPreheat oven to 350°F (175°C). In a bowl, combine graham cracker crumbs, melted butter, and sugar. Press the mixture firmly into the bottom of a 9-inch springform pan. Bake for 10 minutes, then let cool while preparing the filling.Step 2: Cook the Apple FillingIn a skillet over medium heat, melt the butter. Add the sliced apples, brown sugar, cinnamon, and nutmeg. Cook for about 10 minutes, stirring occasionally, until apples are tender and caramelized. Remove from heat and allow to cool slightly.Step 3: Make the Cheesecake BatterIn a large bowl, beat the cream cheese and sugar until smooth and creamy. Add the eggs one at a time, mixing well after each. Stir in the vanilla extract until fully combined.Step 4: Assemble the CheesecakeSpread the apple filling evenly over the cooled crust. Pour the cheesecake batter on top and smooth out the surface with a spatula.Step 5: BakePlace the cheesecake in the oven and bake for 55–60 minutes, or until the center is just slightly jiggly. Turn off the oven, crack the door open slightly, and let the cheesecake sit inside for 1 hour.Step 6: Chill & ServeRemove the cheesecake from the oven and allow it to cool to room temperature. Cover and refrigerate for at least 4 hours or overnight. Just before serving, drizzle the top generously with caramel sauce.