Cioppino, the tomato-rich fish stew of the San Francisco Italian community, borrows its name from this classic Genoese fish soup, but while cioppino is a fish and shellfish stew, ciuppin is a thick puréed or sieved soup, not unlike the Provençal soupe de poisson.
Cook onions, celery, carrot, garlic, and parsley in a pot in olive oil over low heat until onions are soft and translucent, about 15 minutes. Add anchovies and tomatoes and continue cooking about 10 minutes longer.
Add wine, turn heat to high, and cook for about 5 minutes, stirring constantly. Reduce heat to low again, add fish and 3 cups hot water, and cook for 20 minutes, uncovered, until fish is tender and liquid has reduced slightly.
Strain the liquid into another pot, then pass the fish and vegetables through a food mill to obtain a thick, smooth purée. Whisk purée into the liquid and season to taste with salt and pepper. Cook over low heat for about 5 minutes longer.
Put 1 slice of bread in each of 6 bowls and ladle the soup over them.