Preheat the oven to 400°F (200°C).
Spread the sliced mushrooms and onions on a baking sheet.
Drizzle with olive oil and season with salt and pepper.
Roast for about 20 minutes, stirring halfway through, until tender and lightly caramelized.
Melt the butter in a large skillet over medium heat.
Assemble each Grilled Cheese with Gouda by placing shredded Gouda on one bread slice, followed by the roasted mushrooms and onions, then another layer of Gouda. Season lightly with salt and pepper if desired.
Top with the second bread slice and gently press together.
Lightly coat both sides of each sandwich with melted butter by briefly dipping and flipping.
Cook for about 2 minutes per side, flipping carefully, until the bread is golden brown and the cheese is completely melted.
Slice and serve immediately while hot.