1-Melt 2 tablespoons of the unsalted butter in a large skillet over medium-high heat. Add the sliced onions, season with kosher salt and black pepper, cover, and cook until softened, about 3 to 5 minutes.

2-Uncover, reduce the heat to medium-low, and cook, stirring occasionally, until the onions turn deep golden brown, about 20 to 25 minutes. If the onions seem dry, add a bit of water to prevent burning. For extra flavor, add the 2 teaspoons of sherry, red-wine, or white-wine vinegar to deglaze the skillet, cooking until the liquid evaporates, about 1 minute.

3-Transfer the caramelized onions to a medium bowl and season to taste. Stir in the 4 ounces of grated Gruyère cheese to mix well. Place two slices of bread on a surface, spread half of the cheese-onion mixture on each, and top with the remaining bread slices, pressing gently.

4-Melt 1 tablespoon of the remaining butter in the skillet over medium heat. Cook the sandwiches until the bottoms are golden brown, about 3 to 4 minutes, adjusting the heat as needed. Add the last tablespoon of butter, flip the sandwiches, press down, and cook until the cheese melts and the other side is golden brown, about 3 to 4 minutes.

5-Serve immediately for the best taste and texture. For variations, such as vegan options, use plant-based substitutes at the appropriate steps to maintain the dish’s appeal.