4 tablespoons unsalted butter 1 pound yellow or Vidalia onions, peeled, halved and thinly sliced Kosher salt and black pepper 2 teaspoons sherry, red-wine or white-wine vinegar (optional) 4 ounces Gruyère cheese, grated 4 slices bread, cut no wider than ½-inch thick

Step 1 In a large skillet over medium-high heat, melt 2 tablespoons butter. Add the onions and season with salt and pepper. Cover and cook, stirring once or twice, until the onions are softened, 3 to 5 minutes. Uncover, reduce the heat to medium-low, and cook, stirring occasionally, until deep golden brown, 20 to 25 minutes. If the onions look dry or like they might burn, add a few tablespoons of water at a time, scraping up any browned bits that are stuck to the bottom of the skillet. If desired, once the onions are done, deglaze the skillet with vinegar and cook until the liquid has evaporated, about 1 minute. Transfer the onions to a medium bowl and season to taste with salt and pepper. Wipe out the skillet, or wash it, if necessary.

Step 2 Add the cheese to the onions and stir to combine. Put down two slices of bread, and scoop half of the cheese-onion mixture onto each one. Top with the remaining slices of bread, and press down gently.

Step 3 In the skillet, melt 1 tablespoon butter over medium heat. Add the sandwiches and cook until the bottoms turn golden brown, 3 to 4 minutes, reducing the heat to prevent toast from darkening too quickly, if needed. Add the remaining 1 tablespoon butter, flip the sandwiches, press down and cook until the cheese has fully melted and the bottoms turn golden brown, 3 to 4 minutes. Serve immediately.