With motor running, drop garlic through the feeder tube of a food processor to mince. Scrape down sides of bowl. With motor running, add oil through feeder tube; continue to process.
Transfer to a small bowl, stir in thyme and set aside. Switch to the slicing blade and slice the potatoes (or thinly slice them with a knife).
Brush a little of the garlic oil over the bottom of a 9-by-13-inch (or similar size) baking dish. Make 4 layers in this order: potatoes, a generous brushing of the oil, a sprinkling of salt and pepper. Slowly add broth at one corner to avoid washing off garlic and herbs.
Bake until most of the broth has been absorbed, about 45 minutes. To brown, move pan to middle rack and broil until spotty brown, about 5 minutes.
Let rest so potatoes continue to absorb liquid, about 10 minutes. May be made ahead, held at room temperature while roast cooks, then reheated.
