In a stockpot, heat the olive oil over medium high heat and add the garlic and onion. Cook over medium high heat until the onion and garlic are slightly browned and softened, about 5 minutes. Add celery and cook 5 minutes more. Stir in the vinegar and reduce it to almost nothing.
Add the wine and 3 cups of water and bring to a boil. Carefully place the fish into the liquid with 1/2 the parsley and reduce the heat to a high simmer. Cover loosely and cook until the fish is completely cooked through, about 15 to 20 minutes.
Note that you will not stir this. The fish should be served whole. During the last 5 minutes of cooking, add the mussels. When the mussels open, stir in the remaining parsley and serve immediately, drizzled with additional olive oil if desired.
Recipe copyright 2001, Mario Batali. All Rights Reserved.