Spread bread cubes on a baking sheet, and let dry overnight. Alternatively, heat in a 250 degrees F (120 degrees C) oven until dry, about 1 hour.
Preheat oven to 375 degrees F (190 degrees C). Butter a 2 quart baking dish.
Melt butter in a large skillet over medium heat. Saute celery and onions for about 10 minutes. Add mushrooms, and continue cooking for about 8 minutes, or until tender. Season with rosemary, tarragon, chives, parsley, salt, and pepper. Fold in bread cubes, and add enough broth to moisten. Transfer to prepared dish, and cover with foil.
Bake in preheated oven for 40 minutes. Remove cover, and bake for 10 minutes, or until top is crisp.