Heat a large skillet over a medium-high flame. Once the skillet feels hot from 1 inch away, add the olive oil to heat. Add the onions and cook, stirring often, until translucent. Add the mushrooms and continue sautéing until the onions have caramelized and the mushrooms are cooked through. Transfer to a plate to cool slightly.

To assemble the sandwiches, layer the mushroom mixture with the cheese between two slices of bread. Return the skillet to the stove over a medium flame and melt 1 tablespoon of butter.

Place 1 or 2 sandwiches in the pan (depending on space) and fry the sandwiches, on each side until brown and the cheese has melted.

Add butter to the skillet in between every sandwich. Serve hot.