Delicious Doctored Dressing

Name: Delicious Doctored Dressing
Ingredients: 2 tablespoons butter, plus more for the baking dish; 2 tablespoons oil; 2 cups finely diced celery; 2 carrots, peeled and finely diced; 1 large onion, finely diced; 1 fennel bulb, finely diced; 3 cloves garlic, minced; 1 cup cubed peeled celery root; 1 cup cubed peeled parsnips; 1 cup cubed peeled turnips; One 12-ounce package herb seasoned cubed stuffing mix, such as Pepperidge Farm; 2 cups chicken broth, plus 1/2 cup more if reheating; 1/4 cup fresh parsley, finely chopped; 1/4 teaspoon kosher salt; 1/4 teaspoon freshly ground black pepper