Step 1: Preheat your oven to 325°F (160°C). Mix graham cracker crumbs, melted butter, and 1/4 cup sugar. Press into a 9-inch springform pan and bake for 10 minutes.
Step 2: In a large bowl, beat the softened cream cheese and 1 cup of sugar until smooth and airy.
Step 3: Add vanilla extract, then add eggs one at a time, mixing on low speed just until combined.
Step 4: Pour the batter over the pre-baked crust. Place the pan in a larger roasting pan and fill the roasting pan with hot water halfway up the sides of the cheesecake pan.
Step 5: Bake for 70-75 minutes until the edges are set but the center still jiggles slightly. Turn off the oven and let the caramel apple cheesecake sit inside with the door cracked for 1 hour.
Step 6: While cooling, sauté diced apples with brown sugar and cinnamon in a small skillet over medium heat until tender (about 5-7 minutes).
Step 7: Chill the cheesecake for at least 6 hours. Before serving, top with the sautéed apples and drizzle generously with caramel sauce.