1. Preheat the oven to 325°F and lightly grease a 9-inch springform pan.

2. In a bowl, mix the graham cracker crumbs, melted butter, and 2 tablespoons granulated sugar until evenly combined.

3. Press the crust mixture firmly into the bottom of the prepared pan and bake for 8 minutes. Let it cool slightly.

4. In a large mixing bowl, beat the softened cream cheese until smooth and creamy.

5. Add 3/4 cup granulated sugar and mix until fully incorporated.

6. Blend in the sour cream and vanilla extract until smooth.

7. Add the eggs one at a time, mixing on low speed just until combined after each addition.

8. Pour the cheesecake filling over the cooled crust and smooth the top.

9. Bake for 50 to 60 minutes, until the edges are set and the center still has a slight jiggle.

10. Turn off the oven, crack the oven door, and let the cheesecake rest inside for 30 minutes.

11. Remove the cheesecake and let it cool to room temperature, then refrigerate for at least 6 hours or overnight.

12. In a saucepan over medium heat, combine the sliced peaches, brown sugar, lemon juice, cornstarch, and water.

13. Cook for 5 to 7 minutes, stirring gently, until the peaches soften and the sauce becomes glossy and thickened.

14. Let the peach topping cool completely.

15. Spoon the cooled peach topping over the chilled cheesecake before serving.

16. Add whipped cream on top if desired, then slice and serve cold.