Mushroom and Walnut Stuffing

Name: Mushroom and Walnut Stuffing
Ingredients: 2 tablespoons extra-virgin olive oil, plus more for baking dish; 2 large yellow onions, diced small; 3 celery stalks, diced medium (about 2 cups); Coarse salt and ground pepper; 10 ounces cremini or button mushrooms, diced small; 2 tablespoons fresh sage leaves, finely chopped; ½ cup dry white wine, such as Sauvignon Blanc; 1 cup toasted walnuts, roughly chopped; 1 loaf crusty white bread, cut into ¾-inch pieces (8 cups) and left uncovered overnight or toasted; 1 to 1 1/2 cups low-sodium or homemade chicken or turkey broth; 2 large eggs, lightly beaten