Trim 1/2 inch off the stem and top ends of the artichokes. Pull off the toughest outer leaves. With kitchen scissors cut off the prickly points of the remaining leaves.
In a large nonreactive pot, combine the artichokes, wine, onion, lemon slices, oil, garlic, peppercorns, Pernod, bay leaves and salt. Bring to a boil, then lower the heat slightly and simmer briskly until the artichokes, when tested with the tip of a paring knife from the stem end, are tender, about 50 minutes. Remove from the water and set aside to cool. Reduce liquid to simmer.
Meanwhile, in another large pot, bring water to boil for your potatoes. Season with salt. Add the potatoes and cook until fork tender, about 12-15 minutes. Remove from the water with a slotted spoon and set aside to cool. Reduce water to simmer.
In simmering potato water, add the cauliflower, and cook about 5 minutes, until tender. Remove from the water and set aside to cool.
Add the green beans to the same water, and cook about 5 minutes, until tender. Drain and set aside to cool.
Once the vegetables are cool, slice the potatoes in half. Cut the cauliflower into bite-size florets. Cut the eggs into quarters. Remove the artichoke leaves (I like to save them to eat with any extra aioli the next day), discard the center choke (prickly bits), quarter and serve the hearts.
In the simmering artichoke liquid, add the mussels, cover the pot with lid, and steam 2 minutes. Check the mussels, and remove any that have opened to set aside. Continue cooking, removing mussels as they opens so as not to overcook. Discard any that do not open after 10 minutes. Let mussels cool.
Add cod to the same liquid, and cover with lid. Gently poach until just cooked through, about 7 minutes. Remove the cod and set aside to cool.
Return liquid to a boil, add shrimp, and cook just until pink, about 3 minutes. Drain and submerge in ice water for about 3 minutes. Remove and pat dry with paper towels.
In a small serving bowl, add your aioli and center on a large serving platter. Arrange the vegetables and seafood around the aioli in loose, but neat bundles. Serve with lots of lemon wedges.