Put oven racks in upper and lower thirds of oven and preheat oven to 350°F.
Spread bread in 2 large shallow baking pans and bake in upper and lower thirds of oven, stirring occasionally and switching position of pans halfway through baking, until dry, 20 to 25 minutes total. Transfer bread to a large bowl.
Increase oven temperature to 450°F and butter a 13- by 9-inch baking dish (3-quart capacity).
Pour boiling-hot water over porcini and soak 20 minutes, then drain in a fine-mesh sieve set over a bowl, squeezing porcini and reserving soaking liquid. Rinse porcini under cold water to remove any grit, then squeeze out excess water and coarsely chop.
While porcini soak, heat butter (1 stick) in a 12-inch heavy skillet over moderately high heat until foam subsides, then cook white mushrooms, onion, and shallots, stirring occasionally, until golden, 15 to 20 minutes. Add celery, carrots, garlic, and porcini and cook, stirring, 5 minutes. Stir in thyme, sage, parsley, salt, and pepper, then add vegetables to bread, tossing to combine.
Add 1 cup reserved porcini-soaking liquid to skillet and deglaze by boiling over high heat, stirring and scraping up brown bits, 1 minute. Add remaining soaking liquid and salt and pepper to taste and pour over bread mixture, tossing to coat evenly.
Spread stuffing in baking dish and cover tightly with buttered foil (buttered side down), then bake in upper third of oven until heated through, about 20 minutes. Remove foil and bake stuffing until top is browned, 10 to 15 minutes more.
• Stuffing can be assembled (but not baked) 2 days ahead and chilled, covered.
• Stuffing can be baked 6 hours ahead and kept, uncovered, at room temperature. Reheat, uncovered, in a 350°F oven (with sweet-potato brûlée, if making) until hot, about 30 minutes (test center with a wooden pick for warmth).