Use potatoes at least 1½ inches in diameter. Do not use a glass baking dish, which could shatter.

Adjust oven rack to upper-middle position and heat oven to 500 degrees. Square off ends of potatoes and cut crosswise into 1-inch-thick disks. Toss potatoes with butter, thyme, salt, and pepper. Arrange potatoes in single layer in 13 by 9-inch baking pan.

Roast potatoes until bottoms are beginning to brown around edges, about 15 minutes. Remove pan from oven. Using flat metal spatula and tongs, loosen potatoes from bottom of pan and flip. Continue to roast until browned on second side, about 15 minutes longer.

Remove pan from oven, flip potatoes once more, and add broth and garlic. Roast until potatoes are tender and sauce has reduced slightly, about 15 minutes. Baste potatoes with sauce before serving.