Preheat oven to 400 degrees F. Line a 15x10x1-inch baking pan with foil; set aside. In a large bowl combine peach slices, butter, and brown sugar. Transfer peach mixture to prepared pan and roast about 20 minutes or until tender; cool. Chill peaches until ready to use.
Meanwhile, place cheesecake cubes on a waxed paper lined pan and freeze at least 2 hours or until firm.
Place ice cream in a large bowl and stir with a wooden spoon to soften. Stir in frozen cheesecake cubes and half of the cooled roasted peaches. Transfer ice cream mixture to a freezer-safe container and freeze a few hours or until firm. To serve sundaes, top scoops of ice cream with remaining peaches and sprinkle with graham cracker pieces.