Step 1 Slice the onions in 1/2-inch rings, keeping the rings whole as much as possible. Put them in a large skillet and cover them with the oil. Cook over low heat 15 minutes.
Step 2 Pare the artichokes as described, leaving them whole and keeping them in a bowl of lemon water until ready to use.
Step 3Add the carrot and garlic to the onions, cover and cook over low heat until the onions are softened, 15 minutes more.
Step 4Add the artichokes to the skillet, cover and cook over low heat 5 minutes.
Step 5While the artichokes are cooking, combine the fennel seeds, peppercorns, salt, bay leaves, vinegar and wine in a small saucepan and bring to a full boil. Pour the mixture over the artichokes in the skillet and add enough water so the liquid comes about 2/3 of the way up the sides of the artichokes. Cover and cook at a fast simmer until the artichokes are tender enough that a small sharp knife penetrates the base easily, about 20 minutes.
Step 6With a slotted spoon, remove the artichokes to a bowl. Increase the heat to high and cook until the liquid has reduced to a light syrup. You'll know it's done when the liquid barely covers the bottom of the pan and begins to stick slightly.
Step 7Pour the liquid over the vegetables, cover tightly and refrigerate about 30 minutes or until ready to use. The artichokes are best served cool, or at room temperature.