Preheat your oven to 350 degrees F.

Place the bread cubes on a baking sheet and toast them until golden brown, which should take about 15 minutes. Once done, remove the bread cubes from the oven and allow them to cool.

Meanwhile, melt the butter in a large skillet over medium heat.

Add the onions, celery, and carrots, and cook until the vegetables are softened, about 10 minutes.

Incorporate the garlic and mushrooms, continuing to cook for another 5 minutes until everything is fragrant and the mushrooms have softened.

In a large mixing bowl, combine the cooled toasted bread cubes with the sautéed vegetables, chopped parsley, and rosemary.

Pour the vegetable broth over the mixture, stirring gently to ensure the bread cubes are evenly moistened.

Fold in the beaten eggs and Parmesan cheese into the stuffing mixture, and season with salt and freshly ground black pepper to taste.

Transfer the stuffing mixture to a greased 9x13-inch baking dish. Cover the dish with aluminum foil and bake in the preheated oven for 30 minutes.

Remove the foil and continue baking for another 15-20 minutes, or until the top of the stuffing is golden brown and crispy.

Remove the stuffing from the oven and let it sit for 10 minutes before serving.