Preheat grill or grill pan.
Working in batches, cut potatoes into 1/8-inch thick rounds and in a large bowl toss with oil, dill, thyme, and salt and pepper to taste. Grill potato rounds in batches over moderate heat, turning them occasionally, until tender, about 10 minutes, and transfer them to another large bowl. Alternatively, roast potatoes in a 450 degree oven: Arrange half of oiled potatoes, lightly overlapping, in 2 large shallow baking pans and roast in upper and lower thirds of oven, turning them occasionally, until golden and tender, about 15 minutes. Roast remaining potatoes in the same manner