Preheat oven to 350°F (175°C). Wrap the bottom of a 9-inch springform pan tightly with heavy-duty aluminum foil to prevent water seepage if using a water bath later.

In a medium bowl, combine the crushed graham crackers, 1/4 cup granulated sugar, and melted butter. Mix until well combined and crumbly.

Press the mixture firmly into the bottom of the prepared springform pan. Bake for 8-10 minutes, or until lightly golden. Remove from oven and let cool slightly while preparing the filling. Reduce oven temperature to 325°F (160°C).

In a large mixing bowl, using an electric mixer on medium speed, beat the softened cream cheese until smooth and creamy, scraping down the sides of the bowl as needed.

Gradually add 1 cup granulated sugar and the 2 tablespoons all-purpose flour, beating until just combined and no lumps remain.

Beat in the sour cream and vanilla extract until smooth.

Add the eggs one at a time, beating on low speed after each addition just until combined. Do not overmix, as too much air can cause cracks.

Pour the cheesecake batter over the cooled crust in the springform pan.

Place the springform pan in a large roasting pan. Fill the roasting pan with about 1 inch of hot water to create a water bath.

Carefully transfer the roasting pan with the cheesecake to the preheated 325°F (160°C) oven. Bake for 60-70 minutes, or until the edges are set but the center still jiggles slightly when gently shaken.

Turn off the oven, crack the door open slightly, and let the cheesecake cool in the oven for 1 hour. This helps prevent cracking.

Remove the cheesecake from the water bath and the roasting pan. Let it cool completely on a wire rack at room temperature.

Once completely cooled, cover the cheesecake with plastic wrap and refrigerate for at least 4 hours, or preferably overnight, to allow it to set fully.

About 30-45 minutes before serving the cheesecake, prepare the apple crisp topping. In a medium bowl, combine the diced apples, brown sugar, 1 tablespoon all-purpose flour, cinnamon, and nutmeg. Toss to coat the apples evenly.

In a separate small bowl, combine the rolled oats. Add the cold, cubed butter and use your fingertips or a pastry blender to cut the butter into the oats until the mixture resembles coarse crumbs.

Spread the apple mixture evenly into a small oven-safe dish or a pie plate (about 8-inch). Sprinkle the oat-butter crumble evenly over the apples.

Bake in a preheated 375°F (190°C) oven for 15-20 minutes, or until the apples are tender and the topping is golden brown and bubbly.

Remove from the oven and let cool slightly for about 5-10 minutes.

Once the cheesecake is fully chilled and set, carefully remove the springform pan sides.

Spoon the warm apple crisp topping over individual slices of cheesecake just before serving.