• Begin by preheating your oven to 400°F. Arrange one rack near the broiler and the other in the middle of the oven.
• Wash the potatoes thoroughly and make a cross cut approximately 1/4-inch deep on the top of each, ensuring a half-inch border remains. Position them cut-side up on the middle rack and bake for roughly 2 hours until they achieve a crispy texture.
• About 30 minutes before the potatoes are done, thinly slice the onions (about 4 cups). Strip the thyme leaves to obtain around 1 tablespoon. Crush the garlic and grate the Gruyère cheese.
• In a sturdy skillet, heat 2 tablespoons of butter over medium heat. Add the onions, thyme, 1/2 teaspoon of salt, and 1/2 teaspoon of pepper. Cook while stirring frequently, until the onions become tender and turn a golden hue, which should take about 25 to 30 minutes.
• Introduce the minced garlic and 1 tablespoon of flour into the pan, cooking for an additional minute until the mixture begins to brown. Next, add the beef broth and use a spatula to scrape up any browned bits from the bottom of the skillet. Allow this to boil and then reduce to a simmer until thicker, around 3 minutes.
• Take the skillet off the heat and mix in the balsamic or sherry vinegar. Adjust the flavor with extra salt and pepper if necessary.
• Once the potatoes are baked, remove them from the oven carefully using tongs. Deepen the cuts slightly and gently press on both ends to open them up and release steam.
• Return the opened potatoes to the oven for an additional 10 minutes on the lower rack. After this, open them fully and add a portion of the remaining butter to each. Season with a sprinkle of salt and pepper before equally distributing the onion mixture on top and finishing with the grated cheese.

For Broiling:

• Change the oven settings to broil, repositioning the baking sheet to the upper rack. Broil for 3 to 4 minutes, or until the cheese is melted and bubbling. Optionally, garnish with fresh thyme before serving.