Preheat oven to 325°F (163°C). Wrap the outside of a 9-inch springform pan with two layers of heavy-duty foil. Stir together graham cracker crumbs, 1/4 cup granulated sugar, and melted butter. Press firmly into the bottom and 1 inch up the sides of the pan. Bake for 10 minutes, then cool.
In a large bowl, beat cream cheese and 1 cup granulated sugar on medium speed until smooth and fluffy, about 3 minutes. Add eggs one at a time, mixing on low after each just until combined. Blend in sour cream and heavy cream until silky. Pour over the cooled crust.
Place the foil-wrapped pan in a large roasting pan. Pour hot water into the roasting pan until it reaches about 1 inch up the sides. Bake for 60–70 minutes, until edges are set but the center still jiggles slightly.
Turn off the oven, crack the door, and let the cheesecake cool inside for 1 hour. Remove from water bath, discard foil, and cool on a wire rack for 1 hour. Refrigerate uncovered for at least 8 hours or overnight.
In a saucepan over medium heat, combine sliced peaches, 1/2 cup brown sugar, cinnamon, and cornstarch. Cook, stirring gently, until peaches soften and glaze thickens, about 8–10 minutes. Cool completely.
Preheat oven to 350°F (177°C). In a bowl, mix flour and 1/2 cup brown sugar. Cut in cold cubed butter until mixture forms pea-sized crumbs. Spread on a baking sheet and bake for 12–15 minutes, stirring once, until golden. Cool completely.
Spoon cooled peach glaze over the chilled cheesecake. Sprinkle baked crumble on top just before serving.