Arrange one oven rack 6 to 8 inches from the broiler and a second rack in the middle of the oven. Heat the oven to 400°F.

Prepare 4 medium russet potatoes: Scrub the potatoes, then cut a cross shape about ¼-inch deep into each potato, leaving half an inch border. Place the potatoes cut-side up directly onto the middle oven rack. Bake until very crisp and crackly on the outside, about 2 hours.

When the potatoes have about 30 minutes remaining, halve and thinly slice 1 pound yellow onions (about 4 cups). Pick the leaves from ½ small bunch fresh thyme until you have 1 tablespoon. Mince 1 garlic clove. Grate 2 ounces Gruyère cheese on the large holes of a box grater (heaping ½ cup).

Melt 2 tablespoons of the unsalted butter in a 12-inch cast iron or other broiler-safe, heavy-bottomed skillet over medium heat. Add the onions, thyme, ½ teaspoon kosher salt, and ½ teaspoon black pepper. Cook, stirring frequently with a wooden spoon and reducing the heat if the onions start to brown too quickly, until the onions have reduced by over half, are very soft, and deep golden-brown, 25 to 30 minutes.

Add the garlic and 1 tablespoon all-purpose flour and stir until the flour is completely incorporated, leaves a film on the bottom of the skillet, and begins to brown, about 1 minute. Add 1 cup beef broth and scrape up any browned bits on the bottom of the skillet. Increase the heat back to medium if it was lowered while cooking the onions. Bring to a boil. Simmer until the sauce is thickened enough to coat the back of a spoon, about 3 minutes.

Remove the pan from the heat. Add ½ teaspoon balsamic or sherry vinegar and stir to combine. Taste and season with more kosher salt and black pepper as needed.

Carefully remove the potatoes from the oven with tongs and place on a baking sheet. Carefully cut deeper into the cuts you made initially. Gently push the two opposite ends of each potato toward each other to open them, release steam, and expose some of the flesh.

Return the potatoes to the lower oven rack and bake for 10 minutes more. Remove them from the oven. Push the two opposite ends of each potato toward each other again to open them fully. Cut the remaining 2 tablespoons unsalted butter into 4 pieces, and add one piece to each potato. Add a pinch of kosher salt and black pepper to each potato. Evenly divide the onion mixture between the potatoes (about ¼ cup per potato), and top evenly with the cheese.

Turn the oven to broil. Transfer the baking sheet to the upper rack and broil until the cheese is melted, bubbly, and browned in spots, 3 to 4 minutes. Garnish with more fresh thyme leaves if desired.