Preheat oven to 375*. Lightly butter a 9 x 13" baking dish. On a large baking sheet, toast the baguette cubes for about 15 minutes, tossing halfway through, until lightly golden and dry. Place the bread in a large bowl.
In a very large skillet, melt 4 tbsp of the butter. Add onions and celery; cook over medium heat until softened, about 8 minutes. Add sage and thyme; cook until fragrant, about 1. minute. Scrape into the bowl with the bread and wipe out the skillet.
Melt the remaining 4 tbsp of butter in the skillet. Add the mushrooms and cook over medium0high heat until tender and browned, about 8 minutes. Season with salt & pepper. Scrape into the bowl with the bread.
In a medium bowl, mix chicken broth with the egg. Pour over the bread mixture; add 2 tsp of salt and 1/2 tsp pepper. Toss until the bread soaks up the liquid. Scrape into the prepared baking dish and cover with foil. Refrigerate for at least an hour or overnight.
Once the bread is well-saturated, preheat oven to 375*. Bake the stuffing for about 30 minutes, until it is hot throughout. Remove the foil and bake about 30 minutes longer, until the top is lightly golden. Serve warm or hot.