Tip:For the best stuffing, let the bread dry overnight so it can absorb all the other delicious flavors that make it stuffing; toasting the bread also boosts flavor.
Spread the bread cubes in a single layer on a large rimmed baking sheet. Let dry overnight.
Position a rack in the center of the oven and heat the oven to 400°F. Bake the bread cubes until light golden-brown, 12 to 15 minutes.
Heat the butter in a 12-inch skillet over medium-high heat. Add the onions and celery and cook, stirring occasionally, until soft but not browned, 6 to 8 minutes. Let cool. (The recipe may be prepared to this point up to 6 hours ahead.)
In a large bowl, mix the bread cubes with the cooked vegetables, 2 cups of the broth, the parsley, sage, thyme, eggs, 3/4 tsp. salt, and 1/2 tsp. pepper. If the liquid isn’t immediately absorbed by the bread, toss occasionally for a few minutes until it is. If the liquid is immediately absorbed, toss in another 1/2 cup broth. The bread should be moist but not soggy. If necessary, add the remaining 1/2 cup broth.
Butter a 3-quart baking dish (13x9-inch works well). Transfer the bread mixture to the dish, cover with foil, and bake at 400°F until heated through, 25 to 30 minutes. Remove the foil and continue to bake until the top is slightly browned and crusty, about 20 minutes more.