In 2 separate pots, place 1/2 cup white wine. Add mussels to 1 pot, clams to the other, cover both pots and bring to a boil. Reduce the heat to an active simmer and cook until mussels and clams have been steamed open, about 3 to 5 minutes. Remove the shellfish from their respective pots, reserving the cooking liquid, and allow to cool. Once cool, shuck shellfish and discard shells.
Preheat the oven to 400 degrees F.
In a large soup pot, combine the shellfish cooking liquid, vinegar, 1/4 cup oil, anchovies, peppers, onion, celery, carrot and garlic and bring to a boil. Reduce the heat and simmer for 15 minutes. Add the shellfish and stir to heat through.
Meanwhile, toast the bread in the oven for 4 minutes, until light golden brown and crispy. Divide the soup among heated soup bowls, drizzle with a little extra-virgin olive oil, sprinkle with parsley, and serve with a slice of toast floating on top.