Preheat oven to 325°F. Mix graham cracker crumbs, sugar, and melted butter in a bowl until combined and resembling wet sand. Press firmly into the bottom of a 9-inch springform pan. Bake for 10 minutes until lightly golden. Remove and let cool completely.

Beat softened cream cheese on medium speed for 3 minutes until completely smooth and fluffy. Add sugar and beat until well combined, scraping down sides frequently. Add eggs one at a time on low speed, mixing just until incorporated. Mix in vanilla extract and sour cream until smooth. Don't overmix.

Pour cheesecake filling over cooled crust and smooth the top. Wrap outside of springform pan tightly with heavy-duty aluminum foil. Place in a large roasting pan and pour hot water into roasting pan until it reaches halfway up the sides. Bake at 325°F for 55-65 minutes until edges are set but center jiggles slightly. Turn off oven, crack door, and let cool in oven for 1 hour.

While cheesecake bakes, peel and dice apples into small pieces. Melt butter in a large skillet over medium heat. Add apples, brown sugar, and cinnamon. Cook 8-10 minutes, stirring occasionally, until apples are tender. Mix cornstarch with water to make a slurry, stir into apples, and cook 2 more minutes until thickened. Remove from heat and cool completely.

In a medium bowl, mix flour, brown sugar, and oats. Cut in cold butter with a pastry cutter or fork until mixture is crumbly with pea-sized pieces. Spread on a baking sheet and bake at 350°F for 10-12 minutes until golden. Cool completely.

Once cheesecake is completely cool, carefully remove from springform pan. Spread cooled apple topping evenly over the cheesecake. Sprinkle baked crumble over the apples, pressing gently. Drizzle with caramel sauce if desired.

Refrigerate the assembled cheesecake for at least 4 hours or overnight before serving. This allows all the layers to set properly. Slice with a sharp knife dipped in hot water for clean cuts.