Cook the Beef: Start by seasoning 1 lb ground beef with salt and pepper to taste. Form the beef into two evenly-sized patties. Heat a skillet over medium heat and add the patties. Cook until browned and done to your liking, about 6-8 minutes per side. Remove from the skillet and set aside.
Sauté the Veggies: In the same skillet, add 1 tbsp olive oil. Once hot, add 1 cup sliced mushrooms and 1 small onion thinly sliced. Sauté until the mushrooms are golden and the onions are softened, about 5-7 minutes. Remove from the skillet and set aside.
Assemble the Sandwiches: Place two slices of rye bread on a clean surface. Layer each slice with a beef patty, followed by the sautéed mushrooms and onions. Top each with 2 slices of Swiss cheese, then place another slice of bread on top to close the sandwich.
Grill to Perfection: In the same skillet, melt 2 tbsp unsalted butter over medium heat. Carefully place each sandwich in the skillet and grill until the bread is golden brown and crispy, and the cheese is melted, about 3-4 minutes per side. Once done, remove from the skillet and let sit for a minute.
Serve and Enjoy: Slice each sandwich in half and serve warm. Pair it with your favorite sides like fries or a fresh salad!