Combine sugar and water in a large saucepan; bring to a boil, and add butter. Cover and cook over high heat 5 minutes. Uncover and continue cooking until mixture reaches hard ball stage (260°). Remove from heat, and immediately pour syrup onto a buttered marble slab.
Sprinkle oil of peppermint and food coloring over surface of hot syrup; let rest 5 minutes. Begin scraping syrup with metal spatulas into a central mass. Continue scraping and folding until coloring is evenly distributed throughout syrup.
Pull mixture with fingertips, allowing a spread of about 18 inches between hands; fold mixture in half. Repeat this motion rhythmically until consistency of mixture changes from sticky to elastic and glistening.
Begin twisting while folding and pulling. Continue pulling until ridges on the twists begin to hold their shape. This takes 5 to 20 minutes, depending on the weather and your skill.
Shape mint mixture into a 1- inch-thick rope. Using kitchen shears, cut the rope into 1 1/2- inch segments. Twist, pull, and form each segment into desired shapes. Place mints on a wire rack to cool, and cover with a linen towel. Let mints sit overnight or until they become creamy. Wrap mints individually in aluminum foil or place in a sealed container to prevent drying.