Preheat your oven to 325°F.
In a medium bowl, combine graham cracker crumbs, melted butter, and 1/4 cup granulated sugar. Mix until well combined.
Press the mixture firmly into the bottom of a 9-inch springform pan to form the crust. Bake for 10 minutes, then remove from the oven and let cool.
In a large mixing bowl, beat the softened cream cheese with 1 cup granulated sugar and vanilla extract until smooth and creamy.
Add the eggs one at a time, mixing well after each addition. Stir in the sour cream until fully incorporated.
In a separate bowl, combine sliced peaches, cinnamon, and brown sugar. Gently fold the peach mixture into the cheesecake batter.
Pour the cheesecake batter over the cooled crust in the springform pan.
Bake for 55-60 minutes, or until the center is set but still slightly jiggly.
Turn off the oven, crack the door, and let the cheesecake cool in the oven for 1 hour.
Remove from the oven and let cool to room temperature before refrigerating for at least 4 hours or overnight.
To serve, slice the cheesecake and enjoy chilled.