Preheat oven to 350°. Heat oil in a large frying pan over high heat. Cook mushrooms, leeks, garlic, and celery until softened and starting to brown, about 5 minutes. Put mixture into a large bowl; add bread.
Mix broth, eggs, salt, pepper, and parsley in a small bowl and pour over bread. Toss until bread is soaked, then turn into a greased 9- by 13-in. baking dish.
Bake stuffing until it feels firm to the touch and is starting to brown on top, about 45 minutes.
Note: Nutritional analysis is per serving.