Coat the bottom of a metal spatula and a 13-by-9-inch baking dish with butter; set aside. Combine 8 cups of the marshmallows and the butter in a medium pot and cook over medium-low heat, stirring frequently, until melted and smooth, about 8 minutes. Remove from heat and stir in cereal until well coated. Add remaining 3 cups marshmallows and stir just until mixed. Immediately turn mixture into the prepared baking dish and use the buttered spatula to uniformly flatten. Let set up until room temperature and firm, about 45 minutes. Cut into 15 (2-1/2-inch-by-2-1/2-inch) squares and serve.