Preheat oven to 375°F. Spread bread on large rimmed baking sheet. Bake until bread is dry, about 15 minutes. Cool.
Melt the butter in large skillet over medium heat. Add mushrooms and sauté for 6 minutes, until softened. Add green onions, celery, herbs, garlic, salt and pepper and sauté until celery is tender, 6 to 8 minutes.
Keep oven temperature at 375°F. Generously butter a 12-cup muffin tin and set aside. Place bread cubes in very large bowl. Add warm vegetable mixture; toss to combine.
Whisk eggs and broth in medium bowl. Add egg mixture to stuffing and toss to coat. Mix in Parmesan.
Use a ½ cup measuring cup to transfer the stuffing mixture into the prepared muffin tin. Bake, uncovered, for 30-35 minutes, until the muffins are golden brown and crisp. Let cool slightly before using an offset spatula to remove the muffins from the muffin tin.