Tie up the fennel, peppercorns, coriander seeds, bay leaves, and garlic in a cheesecloth bundle and drop into a 2-1/2 quart pot. Add 2 cups water and bring to a boil. Cover, turn heat to low and simmer 20 minutes. Turn off the heat and remove the cheesecloth bundle, squeezing out as much liquid as possible. Add the lemon juice, olive oil, salt, and sugar. Mix and set aside. Halve the lemon. Cut off the long artichoke stems, if there are any.

1. Starting near the stem end, press back the artichoke leaves, one by one, and then snap them off. Keep doing this until you have gone past the bowl part of the artichoke that harbors the heat and have reached the paler inner leaves. Using a sharp knife (a serrated one is particularly good), cut off the remaining leafy area and discard it. Immediately rub all cut sections with a lemon half.

2. Scoop away the "choke" in the center of the artichoke with a grapefruit spoon. Squeeze a little lemon juice into this area and rub it in.

3. Using a sharp paring knife, trim the outside of the artichoke bowl so there are no more dark green sections left and the bowl gets a smooth appearance. Rub these newly cut sections with lemon. Cut each artichoke heart into four, again rubbing cut sections with lemon. Cut and prepare the remaining artichokes the same way.

Peel the potato and cut into sections that seem roughly the same size as the pieces of artichoke heart. Peel the onion and cut it into eight sections. Put the artichoke hearts, potatoes, and onion into prepared liquid and bring to a boil. Cover, lower heat and simmer for about 12 minutes. Remove a piece of potato and a piece of artichoke. Cut off sections of each and taste for doneness and balance of salt and lemon. You may add more of either seasoning at this time if you wish. Cover and simmer another 3 to 7 minutes or until vegetables are tender.

Uncover and cool the vegetables in the liquid. You may refrigerate the contents of the pot if you wish. When serving, remove the cool (or cold) vegetables with a slotted spoon. Do not serve the liquid.