Step 1: Preheat your oven to 350°F (175°C). In a medium bowl, combine graham cracker crumbs, ¼ cup granulated sugar, and ½ teaspoon ground cinnamon. Pour in ⅓ cup melted unsalted butter and mix until crumbs are evenly moistened.
Step 2: Press the crumb mixture firmly into the bottom and slightly up the sides of a 9-inch springform pan. Bake for 8-10 minutes, then remove from the oven and let cool slightly.
Step 3: In a large mixing bowl, beat softened cream cheese on medium speed until smooth and creamy, about 2-3 minutes. Scrape down the sides of the bowl.
Step 4: Gradually add ½ cup granulated sugar and continue beating until light and fluffy, about 2 minutes. Beat in 2 large eggs, one at a time, mixing just until combined after each. Stir in 1 teaspoon vanilla extract.
Step 5: Pour the cheesecake filling over the cooled graham cracker crust in the springform pan. Gently tap the pan on the counter a few times to release air bubbles.
Step 6: In a large skillet, melt 2 tablespoons unsalted butter over medium heat. Add sliced apples. Cook, stirring occasionally, for 5-7 minutes, until apples begin to soften.
Step 7: Sprinkle 2 tablespoons brown sugar, 1 teaspoon ground cinnamon, ¼ teaspoon ground nutmeg, and a pinch of ground cloves over the apples. Stir to combine and cook for another 2-3 minutes, until spices are fragrant and apples are tender-crisp. Remove from heat and let cool slightly.
Step 8: Carefully spoon the cooled spiced apple mixture evenly over the cream cheese filling in the springform pan. Smooth with a spatula.
Step 9: Bake at 350°F (175°C) for 45-55 minutes, or until edges are set but the center still has a slight jiggle. Turn off the oven, crack the door, and let the pie cool in the oven for 1 hour. This slow cooling helps prevent cracks.
Step 10: Remove from the oven and cool completely on a wire rack at room temperature. Once cool, cover loosely and refrigerate for at least 6 hours, or preferably overnight, for best setting and flavor.
Step 11: Just before serving, warm caramel sauce slightly until pourable. Drizzle generously over the top of the chilled pie. Optionally, sprinkle with a pinch of sea salt.
Step 12: Carefully remove the sides of the springform pan. Slice with a sharp, warm knife for clean cuts. Serve immediately.