Cornbread Stuffing

Name: Cornbread Stuffing
Ingredients: 2 sticks unsalted butter, at room temperature, plus more for the baking dish; 3 tablespoons minced fresh sage; 2 tablespoons minced fresh thyme; 2 tablespoons minced fresh parsley; 1 teaspoon minced fresh rosemary; Kosher salt and freshly ground pepper; For the stuffing:; 2 large onions, finely diced; 3 celery stalks, finely diced; 9 cups cubed cornbread (homemade or store-bought); 1 large egg, lightly beaten; 1 cup low-sodium chicken broth; 3/4 cup whole milk