Step 1: Preheat your oven to 350°F (175°C). Wrap the outside bottom of a 9-inch springform pan with heavy-duty aluminum foil to prevent water bath leakage.
Step 2: Make the Crust: In a medium bowl, combine graham cracker crumbs, ¼ cup granulated sugar, and melted butter. Press firmly into the bottom of the prepared springform pan. Bake for 10 minutes. Remove and let cool while you prepare the filling. Reduce oven temperature to 325°F (160°C).
Step 3: Prepare the Cheesecake Filling: In a large bowl, using an electric mixer, beat the softened cream cheese and 1 cup granulated sugar until smooth and creamy. Add the sour cream, flour, vanilla extract, and ½ tsp cinnamon, mixing until just combined. Beat in the eggs one at a time, mixing on low speed until just incorporated. Do not overmix.
Step 4: Pour the cheesecake batter over the cooled crust in the springform pan. Place the springform pan into a larger roasting pan. Fill the roasting pan with hot water to come halfway up the sides of the springform pan. This creates a water bath.
Step 5: Bake for 55-65 minutes, or until the edges are set and the center jiggles slightly when gently shaken. Turn off the oven, crack the door, and let the cheesecake cool in the oven for 1 hour. Remove from the water bath, remove the foil, and cool completely on a wire rack at room temperature.
Step 6: Make the Apple Topping: While the cheesecake cools, melt 2 tablespoons butter in a medium saucepan over medium heat. Add diced apples, brown sugar, ½ tsp cinnamon, nutmeg, and lemon juice. Cook, stirring occasionally, for 8-10 minutes, or until apples are tender-crisp. Let cool completely.
Step 7: Prepare the Crisp Topping: In a small bowl, combine ½ cup flour, rolled oats, ¼ cup brown sugar, and ¼ tsp cinnamon. Cut in the cold butter with your fingers or a pastry blender until coarse crumbs form.
Step 8: Once the cheesecake is cool, gently spread the cooled apple topping evenly over the top. Sprinkle the crisp topping over the apples.
Step 9: Increase oven temperature to 350°F (175°C). Place the cheesecake (without the water bath) back in the oven and bake for 15-20 minutes, or until the crisp topping is golden brown and crunchy.
Step 10: Let the cheesecake cool completely on a wire rack. Then, refrigerate for at least 4-6 hours, or preferably overnight, before carefully removing the springform pan sides and serving.