Notes: Have lobster tails split lengthwise at the market, or use a heavy cleaver to cut through from the softer underside. Or replace lobster with additional shrimp. A dramatic option is whole shrimp (heads on), available in many Asian fish markets. To keep whole shrimp intact, don't shell. To devein, push a thin skewer perpendicularly through back shell under vein, then pull skewer up to lift out vein. Repeat as needed, then rinse shrimp.
Fish, shrimp, and scallops can be cleaned, cut, and chilled up to 4 hours ahead. Chill clams and mussels covered with a damp cloth (not airtight). Scrub shortly before cooking.
1. Mix basil, cilantro, parsley, shallots, and garlic with fish, scallops, and shrimp. Set aside.
2. Bring broth to a boil in a 5- to 6-quart pan over high heat. Add clams and lobster. Cover and simmer until clams open and lobster is barely opaque in thickest part (cut to test), 5 to 10 minutes. As clams open, lift them from the simmering broth with a slotted spoon and keep warm.
3. After 10 minutes, add seasoned fish, scallops, and shrimp to simmering broth. Bring to a boil over high heat, then tightly cover pan and remove from heat. Let stand until shrimp, scallops, and fish are barely opaque in thickest part (cut to test), 3 to 5 minutes. Use in bouillabaisse or, with a slotted spoon, divide seafood equally among wide, shallow bowls. Over high heat, bring broth to boiling, then ladle into bowls.