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Heat the olive oil in a skillet over medium heat. Add the mushrooms and cook for about 6 minutes, until nicely caramelized. Season with salt and pepper. Lay out four slices of the rye bread on a cutting board. Top with half the Swiss, then the onions and mushrooms. Add the thyme (if using) and the remaining cheese. Top with the remaining slices of rye. Spread the softened butter on both sides of the sandwiches. Heat a large cast-iron or nonstick skillet over medium-low heat. Add the sandwiches, working in batches if you must, and cook for 5 to 6 minutes per side, until fully toasted and golden brown.