Cut the carrots, shallots, zucchini, bell peppers, and ham in a "brunoise" fashion (small cubes). Saute all the ingredients in olive oil, in the order given. Do not overcook. Fold in the chopped artichokes. Stuff the 2 artichoke hearts with the filling. Set aside.
On the center of a large platter, place the fig polenta. Arrange the sturgeon around the polenta. Add the stuffed artichoke hearts to the plate. Garnish the plate with chives. Drizzle the platter with the Crustacean Broth and serve.
Trim each artichoke, 1 at a time, to reveal the heart. Cut off the stem and the top of the artichoke, then cut away all the outer leaves in 1 circular motion. Use a spoon to scrape out the pointy thistles, and use the knife to trim away any remaining leaves or husk. You should be left with just the heart (artichoke should be in the shape of a little bowl) Rub the hearts with lemon juice. Place artichokes into a pot of cold water with enough water to cover. Cook on medium heat until a knife easily slides through the artichoke heart, about 15 to 20 minutes. Once artichoke hearts are cool enough to handle, set 2 aside and chop the other 2 into small pieces. You will use the chopped up artichoke for the artichoke filling.
Boil the chicken consomme and the cream. Incorporate the polenta by sprinkling it into the pan. Let it cook for 5 minutes, stirring continuously. Season with salt, pepper, and lemon juice. Add the fig puree.
Heat some olive oil in a pot. When the oil is hot, add the langoustines to heat through. Add the carrot, onion, parsley, thyme, bay leaf, and star anise. Cook for a few minutes. Add the water and powdered licorice. Cook on low heat for 30 minutes. Pass the mixture through a fine strainer and add the cream.