Shiitake Mushroom and Fresh Herb Stuffing

Preheat the oven to 375°. Lightly butter a 9-by-13-inch baking dish. On a large rimmed baking sheet, toast the baguette cubes for about 15 minutes, tossing once halfway through, until lightly golden and dry. Transfer the bread to a large bowl. In a very large skillet, melt 4 tablespoons of the butter. Add the onion and celery and cook over moderate heat until softened, about 8 minutes. Add the sage and thyme and cook until fragrant, about 1 minute. Scrape into the bowl with the bread and wipe out the skillet. Melt the remaining 4 tablespoons of butter in the skillet. Add the mushrooms and cook over moderately high heat until tender and browned, about 8 minutes. Season with salt and pepper. Scrape the mushrooms into the bowl with the bread. In a medium bowl, whisk the chicken broth with the egg. Pour over the bread mixture and add 2 teaspoons of kosher salt and 1/2 teaspoon of pepper. Toss until the bread soaks up the liquid. Scrape into the prepared baking dish and cover with foil. Refrigerate for at least 1 hour or overnight. Preheat the oven to 375°. Bake the stuffing for about 30 minutes, until it is hot throughout. Remove the foil and bake for about 30 minutes longer, until the top is lightly golden. Serve hot or warm.