01 - In a skillet over medium-low heat, melt 1 tablespoon butter with 1 teaspoon olive oil. Add the sliced onion, salt, pepper, and sugar if using. Cook, stirring occasionally, until onions are deeply golden and caramelized, about 20–25 minutes. Remove from heat and set aside.
02 - Lay out the bread slices. Spread a thin layer of softened butter on one side of each slice. Place two slices, buttered side down, on a clean surface.
03 - Top each of the two bread slices with a slice of cheddar, a generous spoonful of caramelized onions, a slice of Swiss or Gruyère, and then finish with the remaining cheddar slices. Close the sandwiches with the remaining bread, buttered side up.
04 - Heat a skillet or griddle over medium heat. Add the sandwiches and cook for 3–4 minutes per side, pressing gently, until bread is golden and crisp, and cheese is melted.
05 - Remove from pan, let rest for 1 minute, then slice in half and serve hot.