1Melt 1 tbsp butter with the oil in a cast iron skillet over medium-low heat. Add the sliced onion, salt lightly, and cook 20 to 25 minutes, stirring now and then, until deep golden and jammy. Scrape onions into a bowl and wipe the skillet clean.
2Gently mix the beef with Worcestershire, a generous pinch of salt, and pepper. Divide into 4 loose balls and press each into a patty about 1/2 inch thick, slightly wider than the bread, with a shallow dimple in the center.
3Set the skillet back over medium-high heat. Sear the patties 3 to 4 minutes per side until browned and cooked through. Transfer to a plate and season with salt and pepper.
4Spread the dressing on one side of each rye slice. Layer Swiss, a patty, a spoonful of onions, and another slice of Swiss on the dressed side of 4 bread slices, then top with the remaining bread.
5Butter the outside of each sandwich with the remaining butter. Cook in the skillet over medium heat 3 to 4 minutes per side, pressing gently, until the bread is golden and the cheese is fully melted. Slice and serve hot.