Preheat oven to 375°F. Spread bread on large rimmed baking sheet. Bake until bread is dry, about 15 minutes. Cool.
Melt 10 tablespoons butter in heavy large skillet over medium heat. Add mushrooms and onion and saute for 5-6 minutes. Add green onions, celery, all the herbs, garlic, salt and pepper and sauté until celery is tender, 6 to 8 minutes more.
Preheat oven to 375°F. Generously grease a large skillet or baking dish. Place bread cubes in very large bowl. Add warm vegetable mixture; toss to combine.
Whisk eggs and 3/4 cup broth in medium bowl. Add egg mixture to stuffing and toss to coat. Mix in Parmesan.
Add more broth (about 1/2 to 3/4 cup) to stuffing if dry. Transfer to skillet or baking dish. Cover with buttered foil. Bake 30 minutes. Remove foil; bake until golden, about 30 minutes.