Heat the oil in a soup pot over medium heat. Add scallions, peppers, onion, and fennel. Cook, stirring occasionally, until the onion is translucent, 6-8 minutes.
Add the garlic and cook, 30 seconds.
Add the white wine, bring to a boil, and cook until the volume of the wine is reduced by about half, 4-6 minutes.
Add the fish broth (we made fresh broth from frozen shrimp shells, fish bones, and aromatics), tomatoes, tomato puree, and bay leaves. Cover the pot and simmer the mixture slowly, about 45 minutes. Add a small amount of water or more broth, if necessary. Cioppino should be more a broth than a stew. Add anchovy paste, paprika, cayenne, season with salt and pepper, and taste, adjusting as you like. If you’re not ready to serve, you can continue to simmer, but once the seafood is added do not delay service. Remove and discard the bay leaves.
Add the clams and simmer about 10 minutes. Discard any clams that do not open. Add the shrimp and fish to the soup. Simmer until the fish is just cooked through, about 5 minutes. Add the crab and basil and adjust the seasoning if necessary.