Preheat your oven to 325°F (163°C). In a medium bowl, combine graham cracker crumbs, 1/4 cup sugar, and melted butter until well mixed. Press this mixture firmly into the bottom of a greased 9-inch springform pan to form an even crust. Bake in the oven for 10 minutes, and then allow it to cool completely while you prepare the filling.

In a large mixing bowl, beat softened cream cheese until completely smooth. Gradually incorporate 1 cup sugar, followed by adding eggs one at a time, mixing well after each addition. Stir in vanilla extract and sour cream until fully combined into a creamy batter. Pour this mixture over the cooled graham cracker crust in the springform pan.

To create a gentle baking environment, place the springform pan into a larger roasting pan. Fill the roasting pan with hot water until it reaches halfway up the sides of the cheesecake pan. Bake for 55 to 65 minutes, until the center of the cheesecake appears slightly jiggly yet set. Turn off the oven, crack the door, and let it cool inside for 1 hour before chilling it in the refrigerator for at least 4 hours or overnight until fully set.

While the cheesecake chills, peel and dice your medium apples. In a skillet over medium heat, melt unsalted butter, then add the diced apples, brown sugar, ground cinnamon, and nutmeg. Stir frequently, cooking for about 8 minutes until the apples become soft and syrupy. Once cooked, set the apple mixture aside to cool completely.

In a medium saucepan, melt granulated sugar over medium heat, stirring constantly until it reaches a deep amber color. Carefully add cubed unsalted butter, mixing until melted, then whisk in heavy cream and a pinch of sea salt. Continue stirring until fully combined and smooth. Allow the caramel sauce to cool slightly before using it for assembly.

After the cheesecake has chilled completely, carefully remove it from the springform pan and place it on a serving plate. Top the cheesecake with the cooled apple mixture, spreading it evenly over the surface. Drizzle the warm salted caramel sauce generously over the apples, allowing it to cascade down the sides. Slice and serve this delicious Salted Caramel Apple Pie Cheesecake, savoring every bite of its indulgent layers.