Preheat oven to 450°F/232°C, with rack in upper middle position.
Cut off just the very end of each potato, so each end is squared. Then cut each potato into about 1-inch thick slices.
In a large bowl, toss the potatoes with the butter, thyme, salt, and pepper. Place potatoes in a single layer in a large ceramic or metal baking dish (don't use a glass dish as it may shatter when adding the broth later).
Roast the potatoes for 20-22 minutes, until bottoms are browning around the edges. Flip each potato slice, then roast another 15 minutes.
Remove pan from oven and flip potatoes again. Add the chicken broth and garlic. Roast once more until the potatoes are tender and sauce has reduced slightly, about 15 minutes.