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Place the clams to soak in salted water in the dark for 3 to 4 hours to allow them to expel all the sand.
Clean the squid in running water. Separate the head from the body. Open the scallops, remove the beards. Remove each scallop from its shell. Rinse. Dry on a towel.
Cut the cuttlefish into 2-inch-sided triangles. Gently score one side of the cuttlefish. Shell the prawns, leaving the head and the tail, but removing the vein.
Wash the broccoli. Remove the heads and peel the stems. Cook the heads in salted boiling salted water, immediately chill in iced water. Drain. Then cook the stems in the same water, and immediately chill in iced water. Set aside the 12 best-looking heads. Using an immersion blender, puree the heads and stems. Add the chicken stock and a drizzle of olive oil, until the puree becomes smooth and silky. Store in a cool place.
Heat a drizzle of olive oil in a pan. Sear the cuttlefish triangles scored-side down for 2 to 3 minutes. Once they have colored slightly, add a knob of butter, and baste. Remove to a cooking crack and keep warm.
Pour the lobster stock in a pan. Heat until it reaches a soft boil. Poach the prawns for 2 to 3 minutes on each side. Place on a cooling rack in a warm place.
Place the clams in a pan. Deglaze with the white wine. Cover the pan. Remove from the heat, and gradually remove them as they open, leaving in the shell. In the same pan, poach the squid for 1 minute. Decant the poaching liquid and reserve.
In a large pan, heat a drizzle of olive oil. Quickly sear the scallops. Add some butter. Finish the cooking process by basting with foaming butter for 4 minutes.
To serve, drain the octopus and place in the saute pan that the clams were cooked in. Add the clams and the broccoli heads. Bind with a drizzle of olive oil. Sprinkle some Espelette powder.
Spread the brocoletti puree on the bottom of the dishes. Then plate the scallops, octopus, squid, cuttlefish, clams and prawns. Lightly reduce the cooking juices if needed, and top the seafood with it. Add 3 drops of lemon juice and a drizzle of olive oil.