01 - In a large skillet over medium heat, melt 1 tablespoon of unsalted butter with 1 tablespoon of olive oil. Add the thinly sliced onions and sprinkle with salt and optional sugar. Cook, stirring frequently, until the onions are soft and deeply golden brown, approximately 20 to 25 minutes. If the onions begin to burn, reduce the heat. Once caramelized, remove from heat and set aside.
02 - Arrange the bread slices on a clean surface. Spread softened butter evenly on one side of each slice. Place two slices, buttered-side down, onto the work surface. Layer each of these slices with 2 slices of cheese and half of the caramelized onions. Season with freshly ground black pepper. Top with the remaining bread slices, ensuring the buttered side faces upwards.
03 - Warm a large skillet or griddle over medium-low heat. Carefully place the assembled sandwiches into the heated skillet. Cook for about 4 to 5 minutes per side, or until the bread is golden brown and the cheese is fully melted. Gently press down with a spatula to ensure even toasting. Remove from the skillet, allow to rest for 1 to 2 minutes, then slice and serve.