Slice the mushrooms and onion into your preferred thickness.
Heat a skillet over medium heat and melt 2 tablespoons of butter.
Add the mushrooms and onions, seasoning with salt and pepper.
Cook until the vegetables become soft and lightly caramelized, about 8–10 minutes.
Transfer the cooked vegetables to a plate.
Butter one side of each slice of bread using the remaining butter.
Assemble each sandwich by placing shredded Gouda on the unbuttered side of one slice of bread, followed by the sautéed mushrooms and onions, then another layer of Gouda. Top with the second slice of bread, buttered side facing out.
Heat the skillet over low to medium heat.
Cook each Gouda Mushroom Onion Grilled Cheese for about 5 minutes until golden brown.
Carefully flip and cook another 2–3 minutes until the cheese is completely melted and both sides are crisp and golden.
Slice and serve immediately.