In a skillet, heat 1 tablespoon of olive oil and 1 tablespoon of unsalted butter over medium heat until shimmering. Add 1 sliced medium onion, sprinkle with salt, and cook for about 15-20 minutes, stirring occasionally.

Once the onions are beautifully caramelized, remove them from the skillet and set aside. Take two slices of your preferred bread, layer shredded Gruyère cheese on one slice, pile on the caramelized onions generously, then top with the second slice of bread.

In the same skillet, melt the remaining tablespoon of butter over medium heat. Carefully place the assembled sandwiches in the skillet, grilling each side for 3-5 minutes until golden brown and the Gruyère cheese begins to melt.

Once both sides of the sandwiches are perfectly grilled and the cheese is melted, transfer them to a cutting board. Slice each sandwich in half and serve warm.