✓ Preheat oven to 350°F (175°C); line a 9‑inch springform pan with parchment.

✓ Combine graham cracker crumbs, ¼ cup granulated sugar, and melted butter in a bowl; stir until mixture resembles wet sand.

✓ Press the crumb mixture firmly into the pan bottom using the back of a spoon; bake for 8 minutes or until lightly golden.

✓ While crust bakes, beat softened cream cheese in a large bowl until smooth; add 1 cup granulated sugar and vanilla extract, mixing until fully incorporated.

✓ Blend in sour cream; mix just until combined to avoid over‑mixing.

✓ Pour the cream cheese filling over the baked crust; smooth the top with a spatula.

✓ Arrange diced apples on the filling, sprinkling lemon juice evenly.

✓ In a separate bowl, mix brown sugar, 1 tsp ground cinnamon, ½ tsp ground cinnamon, flour, and cold butter cubes; use fingertips to crumble until mixture forms coarse crumbs.

✓ Scatter the crumble evenly over the apple layer.

✓ Transfer the pan to the oven; bake for 45 minutes or until the center is set and the crumble turns golden brown.

✓ Turn off the oven, crack the door open, and let the cheesecake cool inside for 1 hour.

✓ Remove the cheesecake from the oven; run a thin knife around the pan edge to release any sticking.

✓ Cool completely on a wire rack for 2 hours, then refrigerate for at least 4 hours or overnight for optimal firmness.

✓ Before serving, run a warm knife around the springform rim and gently unlatch; lift the pan to reveal the finished cake.

✓ Slice with a clean, warmed knife; each piece should show a creamy center, apple chunks, and a crunchy crumble.

✓ Garnish with a dusting of powdered sugar and a sprig of fresh mint if desired; serve chilled.