Peel and chunk the potatoes, then boil them in salted water for 15 to 20 minutes, or until very tender. Drain them thoroughly and mash roughly, leaving a little texture rather than making perfectly smooth potatoes.

While the potatoes cook, melt about 1/2 cup of the butter in a large skillet over medium heat. Add the onion and celery and sauté for 8 to 10 minutes, until softened and fragrant but not deeply browned.

Place the bread pieces in a very large mixing bowl. Add the warm onion-celery mixture, the remaining melted butter, mashed potatoes, poultry seasoning or sage, salt, and black pepper.

Stir in the lightly beaten eggs once the mixture has cooled slightly. Add the milk gradually, starting with 1 1/2 cups, until the stuffing is moist and soft but not soupy; it should hold together when pressed.

Grease a 9-by-13-inch baking dish and transfer the stuffing mixture into it, spreading it into an even layer. Dot the top with a little additional butter for a fragrant, lightly crisp finish.

Bake uncovered at 350°F (175°C) for 45 to 60 minutes, until heated through and lightly browned on top. For a softer, moister center, cover the dish for the first 30 minutes, then uncover it for the remaining baking time.