The bourbon milk punch is a classic new orleans breakfast cocktail, served to hungry locals and hungover mardi gras revelers. Weve seen a million bourbon milk punch variations, calling for everything from ice cream to spiced rum. We favor simplicity here this drinks job is to settle the stomach and cool off a hearty breakfast of grits and spicy sausage. Thats why we like robert hess recipe, from his excellent video series the cocktail spirit. You can use milk, or go with half-and-half or sweet cream. Wed avoid heavy cream; shaking it up will make the drink too thick. If you use milk, it should be full-fat.