In a large mixing bowl combine the beef, garlic, beaten eggs, and salt and pepper, to taste.
Divide the meat mixture into 6 round even patties. Press 1-ounce of blue cheese and 1-ounce of the cold butter into the center of the formed patty. Remold the patty so that all the cheese and butter are hidden inside the center. Continue until all the beef patties have been formed. Refrigerate for 10 to 15 minutes.
Pour the oil into a large skillet over medium-high. When the oil is smoking, add the beef patties and cook on both sides until golden brown. Remove to a sheet pan and roast in the preheated oven until desired doneness is reached, about 6 minutes. Cook's Note: They can be also cooked on a charcoal grill.
Warm the buns slightly, then put the burgers on the buns and top each with lettuce, tomato and an onion ring. Enjoy. You can, if you wish, use mayonnaise, ketchup or mustard to enhance this dish.