Prepare the apple filling by peeling, coring, and slicing the apples. Combine in a saucepan with butter, brown sugar, cinnamon, and lemon juice. Cook until softened, about 10 minutes. Thicken with cornstarch slurry and let cool.

Make the crust by preheating oven to 350°F. Pulse graham crackers into crumbs, mix with sugar and cinnamon, then blend with melted butter. Press into springform pan and bake for 7-8 minutes. Cool completely.

Prepare the cheesecake filling by lowering the oven to 280°F. Beat the cream cheese and sugar until smooth, add vanilla and sour cream, followed by eggs and cornstarch, mixing gently.

Assemble by pouring half of the cheesecake batter into the cooled crust, layering the apple filling, then topping with the remaining batter. Sprinkle with crumble topping.

Bake for 1 hour until edges are set and center is jiggy. Turn off oven, cool with door ajar for 1-2 hours.

Chill wrapped in plastic for at least 5 hours or overnight before serving.