For the Broth
- 3 lobsters (1 to 1 1/4 pounds each)
- 1/4 cup extra-virgin olive oil
- 6 cups chopped fennel (from 2 medium heads), plus fronds, for garnish
- 2 onions, chopped (5 cups)
- 1 celery stalk, chopped (1/2 cup)
- 2 tablespoons tomato paste
- 1 can (28 ounces) crushed tomatoes
- 1 pound bones of white-fleshed fish, such as striped bass, tilefish, or monkfish
- 2 teaspoons saffron threads, crumbled
- 1/2 cup Pernod
- Coarse salt
For the Vegetables
- 12 new or small potatoes, peeled and halved
- Coarse salt
- 3 zucchini
- 3 yellow squashes
- 2 red bell peppers
- 1 yellow bell pepper
- 2 heads fennel, fronds discarded
- 12 cipollini onions, peeled and halved if large
- 2 tablespoons extra-virgin olive oil, divided
For the Seafood
- 12 mussels, scrubbed, beards removed
- 2 pounds skinless striped bass fillet, cut into 12 pieces
- 2 pounds skinless tilefish fillet, cut into 12 pieces
- 2 pounds skinless monkfish fillet, cut into 12 pieces
Make the broth: Bring a large pot of water to a boil. Add lobsters; cook until bright red and partially cooked, about 7 minutes. Remove from water. When cool enough to handle, twist off tails and claws. Remove tail and claw meat; set aside shells and bodies. Cut tail and claw meat into 12 pieces total, and refrigerate.
Heat oil in a large stockpot over medium-high heat. Add fennel, onions, and celery; cook until softened, about 10 minutes. Add tomato paste; cook 1 minute, then stir in tomatoes, lobster bodies and shells, and fish bones. Cover with 1 inch water; add saffron. Bring to a boil. Reduce to a simmer, partially cover, and cook 1 hour 30 minutes. Pour through a fine sieve into a very large bowl (you should have 4 quarts); discard solids. Add Pernod; season broth with salt.
Make the vegetables: Place potatoes in a pot; cover with 1 inch salted water. Bring to a boil. Reduce to a simmer; cook until tender, about 10 minutes. Drain.
Bring a large pot of water to a boil. Cut zucchini and yellow squashes into 2-inch-thick rounds. Add them and 1 tablespoon salt to boiling water. Return to a boil; cook until just tender, about 2 minutes. Drain.
Roast peppers over the flame of a gas-stove burner or under a broiler, turning often, until charred on all sides, about 8 minutes. Transfer to a bowl, and cover with plastic wrap. Let stand 5 minutes. Peel, and discard stems, seeds, and ribs. Cut flesh into 2-inch pieces.
Trim fennel, then halve, and remove cores. Separate into leaves; cut into 2-inch pieces. Peel cipollinis, and halve if large. Heat 1 tablespoon oil in each of 2 pots over medium heat. Add fennel and 1 teaspoon salt to 1 pot; add onions and 1 teaspoon salt to the other. Cover, and cook, stirring occasionally, until just tender, about 7 minutes for fennel and 9 minutes for onions.
Make the seafood: Place mussels in a pot. Cover, and cook over high heat until they open, 2 to 4 minutes; discard any that do not open. Add strained mussel cooking liquid to broth.
Divide broth among 3 large saute pans or pots. Season fish with salt; add to 1 pan in a single layer. Cook over medium heat until opaque throughout, about 12 minutes. Meanwhile, if vegetables have cooled, combine and heat together in another pan of broth. Reheat lobster in third pan until just warmed through.
To serve, place 1 piece of each kind of fish, 1 piece of lobster, and 1 mussel in each of 12 bowls. Divide vegetables among bowls; ladle hot broth over all. Garnish with fennel fronds, and serve immediately with rouille.