Preheat oven to 375°F. Spread the cubed bread on large rimmed baking sheet and transfer into the oven. Bake until bread is dry, about 15 minutes. Remove from the oven and let cool.
Meanwhile, melt the butter in heavy large skillet over medium heat. Add mushrooms and shallots and saute until golden, about 7 minutes. Add the celery, green onions, various herbs, garlic, salt and pepper and sauté for 3-4 minutes more.
Generously grease a large baking dish.
Place the bread cubes in large bowl. Add the warm vegetable mixture; toss to combine.
Whisk the 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 it still looks and feels dry. Transfer to skillet or baking dish. Cover with buttered foil. Bake 30 minutes. Remove foil; bake until golden, about 30 minutes.