Mix together the beef, minced onion, potato, salt and pepper. Shape the mixture lightly into 6 patties. Place in a generous amount of hot butter in a large iron skillet and brown on both sides. Brown the onion slices briefly in the same skillet. Arrange an onion slice on a tomato slice, place the hamburgers on top, and serve with Bearnaise or mustard sauce.
My own favorite way to serve hamburgers is to cook the meat, lightly seasoned with onion, salt and mixed with an egg, in a hot pan, browning the patties quickly on both sides. During the last minute or two, add a good-sized piece of butter, some sliced mushrooms, Worcestershire sauce, and white wine. Remove the hamburgers to hot plates, pour the sauce over them, and serve with grilled tomatoes.