Preheat the oven to 350°F (175°C). Grease a 9-inch springform pan and set aside.

In a large bowl, beat the cream cheese, granulated sugar, and vanilla until smooth and free of lumps. Scrape the bowl as needed.

Add the eggs one at a time, beating until incorporated before adding the next.

Stir in the sour cream until smooth.

Pour the batter into the greased pan and smooth the top.

Heat a skillet over medium heat, add butter, then the sliced peaches and brown sugar. Cook until the peaches soften and the sugar becomes syrupy (about 6–8 minutes). Remove from heat and cool slightly.

Spoon the warm peaches evenly over the cheesecake batter.

In a small bowl, combine crushed graham crackers, melted butter, and cinnamon until moistened.

Sprinkle the crumble evenly over the peaches.

Bake for 50–60 minutes, until the edges are set and the center has a slight jiggle but is not liquid.

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

Cool to room temperature, cover, and refrigerate for at least 4 hours (preferably overnight) before serving.