1: Cook the bacon: Set up your grill for direct grilling and heat to medium. (Leave a third of the grill as a safety zone in case of flare-ups.) Brush and oil the grill grate. Lay the slices of bacon perpendicular to the bars and grill, turning once or twice with tongs, until the bacon is browned and crisped, about 20 minutes. Alternatively, cook the bacon in a cast iron skillet on your grill’s side burner, in the oven (375 degrees) on a wire rack over a rimmed sheet pan, or on the stovetop.
2: Divide the meat into six equal portions. Lightly wet your hands with cold water, then form each portion of meat into a round patty, 4 inches across and of an even thickness.
3: If you haven’t done so already, set up the grill for direct grilling and heat to medium-high.
4: When ready to cook, brush and oil the grill grate.
5: If using onion slices, brush them on both sides with melted butter and season with salt and pepper. Place the onion on the hot grate and grill until nicely browned, about 4 minutes per side, then transfer to a plate.
6: Brush one side of the meat patties lightly with melted butter and season with salt and pepper. Arrange the burgers, buttered side down, on the hot grate and grill until the bottoms are nicely browned, 4 to 5 minutes. Brush the tops lightly with some of the melted butter and season them with salt and pepper. Using a spatula, turn the burgers. Top each with a slice of cheese, and grill until they are browned and cooked to taste, 4 to 5 minutes longer for medium. Meanwhile, brush the cut sides of the buns with the remaining melted butter and toast them, cut sides down, on the grill during the last 2 minutes the burgers cook.
7: Assemble the sandwiches: Drizzle the bottoms of the buns with the Thousand Island dressing or fry sauce. Top with shredded lettuce or lettuce leaves, the cheese-topped burgers, tomato slices, grilled onions, and cooked bacon. Drizzle with more dressing, then place the top of the bun on the sandwich. Serve immediately.