Preheat oven to 325 degrees. Toast bread in a large rimmed baking sheet until dry, 15 to 20 minutes.
Peel and cook potatoes. Drain and mash. Set aside.
Cook onions, celery, and herbs in butter in a large heavy skillet over moderate heat, stirring occasionally, until celery is softened, about 10 minutes. Stir together bread, mashed potatoes, vegetables, broth, water, and salt and pepper to taste, then cool completely.
Stuffing can be made a day ahead and kept covered and chilled.