Step 1 Peel the shrimp and put the shells in a small saucepan. Cut the onion in half and add half the onion, 2 sprigs of tarragon, black peppercorns and one-fourth teaspoon salt to the shrimp shells. Cover with the water and bring to a simmer. Cook 30 to 45 minutes. This will make about 2 cups of strained broth.
Step 2 While the stock is cooking, clean the artichokes. Have a large bowl at your side filled with water and the juice of half a lemon. This is where you will put the cleaned artichokes; the lemon juice in the water will keep them from discoloring. You will probably need two knives: one medium slicing knife for trimming and a small paring knife for finishing the peeling.
Step 3Hold the artichoke in your left hand with the stem facing toward you and the tip facing away. Slowly turn the artichoke against the sharp edge of the knife while making an abbreviated sawing motion. (It's easier to control if you use the base of the knife rather than the tip.) You will begin to cut through the tough outer leaves; when you can discern the natural cone shape of the artichoke, adjust the knife to follow it. Keep trimming just like this until you've cut away enough of the tough leaves so that you can see only light green at the bases. Cut away the top half an inch or so of the tip of the artichoke and dip the artichoke into the lemon water to keep the cut surfaces from discoloring.
Step 4With the paring knife, trim away the very tip of the stem, then peel the stem and base of the artichoke going from the tip to where the base meets the leaves. You'll have to do this at least five or six times to make it all the way around the artichoke. When you're done, there should be no dark green tough spots left, only pale green and ivory. If you're using baby artichokes, leave the choke whole. Just put it in the lemon water and repeat for the remaining artichokes.
Step 5By the time you've finished all of the artichokes, the shrimp stock will probably be ready. Melt the butter in a large, heavy skillet. Mince the remaining half onion and add it and the shallots to the butter. Cook over medium-low heat until the onions soften, about 5 minutes. Add the wine and cook until it is reduced to a syrup, about 5 minutes.
Step 6Add the artichokes and stir to coat with the flavorings. Add 1 cup of the strained shrimp stock, cover the skillet and raise the heat to medium. Cook, stirring occasionally, until the artichokes are tender enough to pierce with a small sharp knife, 15 to 20 minutes. Season to taste with salt.
Step 7When the artichokes are cooked, there should be only a little moisture left in the pan; if there isn't, add a little more strained broth. Add the cream and stir to swirl it into the remaining liquid. (The recipe can be prepared to this point up to 2 hours in advance or even earlier if tightly covered and refrigerated.)
Step 8When almost ready to serve, bring the artichoke mixture back to a simmer