Green Bean Casserole Stuffing

Name: Green Bean Casserole Stuffing
Ingredients: 1 stick plus 2 tablespoons unsalted butter, plus more for the baking dish; Kosher salt; 12 ounces trimmed green beans, cut into 1/2- to 1-inch pieces; 1 pound white mushrooms, halved and sliced; 2 onions, chopped; Freshly ground pepper; 2 cloves garlic, minced; 2 tablespoons chopped fresh thyme; 2 1/2 cups low-sodium chicken broth; 1 cup heavy cream; 2 large eggs; 16 cups stale white sandwich bread cubes (about 1/2 inch); 1/2 cup grated Parmesan cheese; Fried onions, for topping