Scrub the whelks under cold running water. Transfer to a large saucepan and cover with cold water, the vinegar, cracked black pepper, and 1 tablespoon salt. Bring to a boil, cover, reduce the heat and, simmer, skimming as needed, for 1½ hours. Strain and, when cool enough to handle, pick the meat from the shells. Separately rinse the meat and shells with cold water. Return the shells to the saucepan, cover with water, and boil for 10 minutes. Trim the guts from the meat, leaving just the muscle. Rinse the muscle, pat dry, and toss with olive oil, salt, and white pepper to taste. Strain the shells and chill under cold running water. Return the whelks to the shells for presentation.
For the Lobster and Shrimp
In a large stockpot, bring the court bouillon to a boil and place a large bowl of ice water on the side. Drop the lobsters into the pot, being sure they are submerged (add water if necessary), and cover with a lid. Simmer for 10 minutes. Transfer the lobsters to the ice water to chill. Return the court bouillon to a light simmer and add the shrimp. Poach at just below a simmer for 4 minutes. Chill in the ice water.
Strain and pat dry the lobsters and shrimp. Remove the meat from the claws and knuckles of the lobster. Cut off the tails, slice them in half lengthwise through the shell, and remove the veins. Cut the tail meat into pieces and return to the shells. Peel the shrimp. Reserve the seafood, covered and chilled.
For the Vegetables
Place the potatoes in a medium saucepan, cover with cold salted water, and bring to a simmer. Cook until the potatoes are tender. Strain, peel if desired, and chill in the refrigerator.
In a large stockpot, bring 2 gallons of salted water to a boil and set a bowl of ice water on the side. In separate batches, boil the asparagus, carrots, celery, haricots verts, and broccoli rabe until tender. Allow the water to return to a boil in between batches. Remove and chill the vegetables in ice water, strain, and pat dry.
For the Aïoli Sauce
Cut the cloves of garlic in half lengthwise and remove the germ. In a small saucepan, bring 6 halves of the garlic to a boil in cold water, then discard the water and repeat, cooking the garlic until tender the second time. Fill a small saucepan with a few inches of water and add the vinegar and a pinch of salt; crack the whole egg into a cup. Bring the water to a simmer and slide in the egg. Poach for 2 minutes (the white will solidify but the yolk will remain runny). Transfer the poached egg to a blender or food processor and add the cooked and raw garlic, the egg yolks, mustard, 3 tablespoons water, and ¾ teaspoon salt. Blend until well combined. While the machine is still running, add the olive oil and then the canola oil in slow, steady streams. The sauce should emulsify, with a thick, pale consistency similar to that of mayonnaise. Taste for seasoning, then transfer to a bowl.
Assemble the lettuce, radishes, cooked whelks, lobster, shrimp, and boiled vegetables on a platter. Sprinkle aïoli sauce with piment d’Espelette and serve alongside for dipping.