Trim fat from alligator meat. Cut meat into small medallion-like pieces and tenderize with a meat mallet or bottom of a heavy pan until very thin. Dredge the medallions in seasoned flour making sure the meat is completely coated. Dip each piece into well beaten eggs. In a hot sauté pan, quickly sauté with butter until golden brown on both sides. Drain and serve with Dijon Mustard Sauce.