Step 1: Make the Graham Cracker Crust

1. Prepare the pan: Preheat your oven to 325°F (163°C). Grease a 9-inch springform pan and line the bottom with parchment paper.
2. Mix the crust ingredients: In a medium bowl, combine the graham cracker crumbs, granulated sugar, and melted butter. Stir until the mixture resembles wet sand.
3. Form the crust: Press the crumb mixture firmly into the bottom of the prepared springform pan, creating an even layer. Use the back of a spoon or the bottom of a glass to press it down.
4. Bake the crust: Bake the crust for 8–10 minutes, then remove it from the oven and let it cool while you prepare the cheesecake filling.

Step 2: Make the Cheesecake Layer

1. Beat the cream cheese: In a large mixing bowl, use a hand or stand mixer to beat the softened cream cheese until smooth and creamy (about 2 minutes).
2. Add sugars: Gradually mix in the granulated sugar and brown sugar, beating until fully combined.
3. Incorporate eggs: Add the eggs one at a time, mixing on low speed after each addition to avoid overmixing.
4. Add sour cream and spices: Mix in the sour cream, heavy cream, vanilla extract, cinnamon, and nutmeg until smooth.
5. Fold in peaches: Gently fold the finely diced peaches into the cheesecake batter.
6. Pour into crust: Pour the cheesecake batter over the cooled crust, smoothing the top with a spatula.

Step 3: Bake the Cheesecake

1. Prepare a water bath: Wrap the bottom and sides of the springform pan with aluminum foil to prevent leaks. Place the pan in a large roasting pan and fill the roasting pan with hot water until it reaches halfway up the sides of the springform pan.
2. Bake the cheesecake: Bake at 325°F (163°C) for 55–65 minutes, or until the edges are set and the center has a slight jiggle.
3. Cool gradually: Turn off the oven and leave the cheesecake inside with the door slightly ajar for 1 hour. This helps prevent cracks.

Step 4: Make the Peach Cobbler Topping

1. Prepare the peaches: In a medium saucepan, combine the sliced peaches, granulated sugar, brown sugar, cinnamon, nutmeg, cornstarch, and lemon juice.
2. Cook until thickened: Heat the mixture over medium heat, stirring occasionally, until the peaches are soft and the sauce is thickened (about 5–7 minutes). Remove from heat and let cool.

Step 5: Make the Streusel Topping

1. Mix the dry ingredients: In a small bowl, combine the flour, rolled oats, brown sugar, and cinnamon.
2. Cut in the butter: Add the cubed butter and use a fork or pastry cutter to work it into the dry ingredients until the mixture resembles coarse crumbs.

Step 6: Assemble and Bake the Topping

1. Add the topping: Once the cheesecake has cooled to room temperature, spread the peach cobbler topping evenly over the top. Sprinkle the streusel mixture on top of the peaches.
2. Bake the topping: Return the cheesecake to the oven at 375°F (190°C) for 15–20 minutes, or until the streusel is golden brown.
3. Chill the cheesecake: Allow the cheesecake to cool completely at room temperature, then refrigerate for at least 6 hours or overnight.

Step 7: Serve and Enjoy

1. Release from the pan: Run a knife around the edge of the springform pan to release the cheesecake, then remove the sides of the pan.
2. Slice and serve: Slice the cheesecake with a sharp knife (clean the knife between cuts) and serve chilled or slightly warmed.