Line a broiler-safe 8x8-inch glass or metal baking dish with foil and grease with butter.
In medium bowl, combine 1-1/2 cups graham cracker crumbs, sugar, and butter; press firmly into bottom of prepared dish. Cover and freeze 30 minutes or more. Soften ice cream at room temperature for 5 minutes; remove carton from ice cream and cut ice cream in half. Place both halves on top of frozen crust, trimming, if necessary. Use a spatula to press and spread ice cream evenly. Cover and freeze solid, 30 minutes or more. Preheat broiler with rack in lower part of oven. Remove ice cream cake from freezer; top with marshmallows (tightly placed together), spreading to edges of pan, pressing down to seal. Place cake under broiler, 8 to 10 inches from heating element. Broil until marshmallows are puffed and golden, 2 to 3 minutes, watching constantly. Remove from oven, sprinkle with remaining 1/4 cup graham cracker crumbs, and drizzle with chocolate sauce, if desired; cut and serve immediately. Makes 10 servings.