Fry bacon until crisp. Remove and drain on paper towel. Saute onion in the fat. In a pot, cover fish pieces with water, add parsley, salt, pepper, and simmer until fish is tender, 15 to 20 minutes. Add onions.
Melt butter in a saucepan, stir in the flour, and cook 1 minute. Turn off heat, whisk in milk or cream and stir into fish and liquid. Beat egg yolks, add 2 tablespoons of hot liquid to the yolks, then stir all into the soup. Simmer a few minutes. Add crisp bacon, and serve. Serves 3-4.