Step 1: Preheat your oven to 350°F (175°C). Line a 9x9-inch baking pan with parchment paper, leaving an overhang on the sides for easy lifting.
Step 2: In a medium mixing bowl, combine graham cracker crumbs, ⅓ cup granulated sugar, and melted butter. Stir until moistened. Press firmly into the bottom of the prepared pan. Bake for 8-10 minutes, then cool slightly.
Step 3: In a large bowl, beat softened cream cheese and ½ cup granulated sugar until smooth. Add eggs one at a time, mixing well after each. Stir in vanilla extract until creamy.
Step 4: Pour the cheesecake batter over the slightly cooled crust and spread evenly.
Step 5: In a separate bowl, whisk flour, brown sugar, and cinnamon. Cut in cold, cubed butter with a pastry cutter or fork until crumbly.
Step 6: Toss diced peaches into the crumble mixture, coating them well. Ensure canned peaches are very well-drained.
Step 7: Evenly spoon the peach mixture over the cheesecake layer. Press down lightly to adhere.
Step 8: Bake for 35-40 minutes, or until the cheesecake center is just set and the topping is golden and bubbly. Cool completely at room temperature, then chill in the refrigerator for at least 3 hours or overnight before slicing and serving.