Savory Bread Pudding

Name: Savory Bread Pudding
Ingredients: 5 tablespoons unsalted butter, divided; 1 medium yellow onion, diced into ¼-inch cubes; 2 celery stalks, diced into ¼-inch cubes; Salt and freshly ground black pepper; 3 cups cremini or button mushrooms, coarsely chopped; 2 tablespoons finely chopped fresh thyme leaves; 3 sage leaves, finely chopped; 2 fresh or dried bay leaves, finely chopped; 1 cup chicken livers, cleaned; 2 cups heavy cream; 5 eggs; 1 large rustic loaf of bread, diced into 1-inch cubes (about 8 cups)