Position rack in upper third of oven; preheat to 500°F.

Combine sliced potatoes, 1½ tablespoons oil, the melted butter, 1 tablespoon thyme, ½ teaspoon pepper and ¼ teaspoon salt in a large bowl; toss well to coat. Arrange in a single layer in a 9-by-13-inch metal baking pan. (Do not use a glass dish, which could shatter.) Roast, flipping once, until browned, 35 to 40 minutes.

Meanwhile, place sliced onions and ½ cup water in a large skillet. Cover and cook over medium-high heat, stirring occasionally, until the onions are softened and water has evaporated, about 15 minutes. Uncover the pan and continue to cook, stirring often, until the onions are deeply golden brown and jammy, 20 to 25 minutes, adding additional water as needed if the pan becomes dry. Add 1 tablespoon vinegar; cook, stirring constantly to scrape up any browned bits, until the liquid has evaporated, about 1 minute. Remove from heat.

Combine 1 cup broth and the chopped garlic in a small bowl; carefully add to the pan with the potatoes. Continue roasting, undisturbed, until some of the broth is absorbed and the potatoes are very tender, about 7 minutes more.

Remove the potatoes from oven and place the pan on a heat-safe work surface; immediately add the cubed cold butter. Gently shake the pan back and forth until the butter is fully melted and emulsified. Increase oven temperature to broil.

Top the potatoes with the caramelized onions and sprinkle evenly with ½ cup Gruyère. Broil until the cheese is melted and lightly browned, about 5 minutes. Sprinkle with the remaining ¼ teaspoon salt. Garnish with thyme leaves and/or pepper, if desired.