Heat 2 tablespoons of olive oil in a large pot over medium heat. Add the anchovies and gently smash them into the oil with your spoon until they are almost completed "melted." Add onion and celery and cook until the onion is translucent, about 10 minutes. Add garlic, red pepper flakes, and bay leaf and cook 2 minutes until garlic is fragrant.
Add wine and let simmer about 1 minute while scraping any browned bits from the pot. Add finely chopped tomatoes, chicken stock, parsley, and oregano. Cover and bring to a boil. Reduce the heat to medium-low and simmer covered 45 minutes. Season to taste with salt. At this point, I added 1 teaspoon of Kosher salt. The exact amount you use will vary depending on how salty your anchovies and stock are.
(You can cool the Cioppino tomato base at this point and store in the refrigerator to cook the following day. When ready to finish cooking the dish, return the Cioppino tomato base to a large clean pot, bring to a boil, reduce heat, and proceed as follows.)
Remove bay leaf. Add clams to the pot. Cover and cook until the clams begin to open, about 10 minutes. Add mussels, and cook until they open, about 5 minutes. Add the fish. Simmer gently until the fish is just cooked through, and the clams and mussels are completely open, another 5 minutes. Discard any clams and mussels that do not open.
Taste the tomato base and season with more salt and red pepper flakes if necessary. I added about ½ teaspoon more salt here.
Ladle Classic Cioppino into bowls. Garnish with fresh chopped parsley and basil if using.
Serve with warmed or grilled bread and lemon wedges.