Make the stew base. Heat a large stew pot or Dutch oven over medium heat with the olive oil. Add the onions and saute until tender, about 5 minutes. Add the garlic, season with salt and pepper to taste, and cook 2 minutes more. Stir in the tomato paste and cook for 1 minute. Add the wine, and use a wooden spoon to scrape up any browned bits in the pot. Simmer the wine until reduced by about half. Add the tomatoes, peppers, parsley, thyme, and bay leaf and cook for 5 minutes. Add the stock or broths; bring to a boil, then adjust the heat to maintain a gentle simmer. Cook the base, with a cover slightly ajar, for 30 minutes. (The base may be prepared ahead up to this point, refrigerated for 1 day or frozen for 1 month).

Finish the Cioppino. Bring the base to a simmer. Add the basil and the clams, and cook covered, over high heat, for 5 minutes, or just until the clams open. Add the crab and cook for 1 minute. Add the mussels, shrimp, squid, and scallops. Cook, stirring frequently, until the mussels open, the shrimp curl, and squid and scallops are just firm, about 3 minutes. Serve in large heated bowls with plenty of crusty bread.