Caramelize the Onions: In a medium skillet, heat the olive oil and butter over medium heat. Add the thinly sliced onions, sugar, salt, and pepper. Cook for about 15-20 minutes, stirring occasionally, until the onions are soft and golden brown.

Prepare the Bread: While the onions are cooking, prepare your bread. Lay out the slices on a clean surface.

Add Cheese: On one slice of bread, layer a generous amount of Gruyère cheese followed by a layer of caramelized onions. Top with mozzarella cheese and another slice of bread.

Grill the Sandwich: In the same skillet, add a bit more butter if necessary and place the assembled sandwich on the skillet. Grill for about 3-4 minutes on each side or until the bread is golden brown and the cheese is melted.

Serve: Once grilled to perfection, remove the sandwich from the skillet and cut it in half. Optionally, garnish with fresh thyme or parsley.

Repeat: If making more than one sandwich, repeat the grilling process with the remaining ingredients.