In a large bowl, carefully mix the meats, steak sauce, egg yolks, salt, and pepper with the tines of a fork, but do not mash the mixture. Lightly form hamburger patties and press lightly into shape. Press a thin slice of butter into the top of each hamburger, making sure the meat entirely encases the butter.
Prepare a charcoal or a stovetop grill and cook the hamburgers for 4 minutes on one side, turn, and cook 3 minutes on the other side for medium-rare. Remove to a plate and cover with aluminum foil. Allow the hamburgers to rest for 5 minutes. Meanwhile, grill the buns, cut side down, for 1 minute, until toasted. Place a hamburger and a slice of blue cheese in each bun, plus arugula and tomato serve hot.
Copyright 2006, Barefoot Contessa at Home by Ina Garten, Clarkson Potter/Publishers, All Rights Reserved