One hour before cooking the burgers, form them into patties, salt and pepper them, and leave them out until time to cook them. Don't leave them out more than one hour.
Heat a large non stick frying pan over medium heat. While the pan is heating, melt 1/4 cup of the butter. Brush melted butter over the insides of the buns and place butter side down in the hot frying pan. Reserve any leftover butter. Grill the buns until golden brown. Wrap in tin foil and put in a warm place.
Cut the onion in slices. Heat the frying pan on medium high and add the onions and all of the remaining butter. Cook the onions for one minute before adding the burgers. Cook for 5 minutes on the first side and 3 minutes on the second side for medium rare. Add more time depending on how well done you like your burger. When finished cooking, remove the pan from the heat and cover. This would be a good time to add cheese. Let the burgers rest for 5 minutes before serving on the buttered buns with the onions. Enjoy!