PREPARE THE ARTICHOKES Pull off the small lower leaves around the stem.
Cut the stems to about 3/4 inch.
Using a serrated stainless steel knife, cut off the top 1/4 of the artichoke and, with kitchen shears, cut off the prickly tip of each remaining leaf.
Rinse the artichokes under cool water.
Rub lemon juice over the cut stems or drop them into a bowl of acidulated water to prevent discoloration if they will not be cooked right away.
Fill a nonaluminum pot just large enough to hold the artichokes with about 2 inches of water.
Add 1 tablespoon of vinegar, and the artichokes, stem sides down.
Cover the pot, and bring to a boil.
Boil gently until the leaves pull off easily and the heart is tender when pricked with a fork, about 20 to 40 minutes, depending on the size.
Check from time to time to be sure that the water has not evaporated.
When the artichokes are tender, remove them to a collander and let them drain until cool enough to handle.
Gently pull the leaves apart to reveal the choke.
Lift it off and, with a spoon, carefully scrape off the fuzzy part which remains on the heart.
Put them in a bowl, cover, and set them aside to cool.
make the potato salad In a large saucepan, boil the potatoes just until tender when pierced with a sharp knife, about 14 to 17 minutes.
Drain, peel, and cut them into 3/4 inch cubes.
Transfer the potatoes to a bowl, add the celery, scallions, and dill.
Combine the sour cream, mayonnaise, and vinegar in a small bowl, then add it to the potatoes, and turn gently to mix.
Add the caviar, salt, and plenty of black pepper.
Toss gently.
Spoon the potato salad into the artichokes.
prepare the sauce In a small bowl, combine the cup of mayonnaise with the dill, shallot, and vinegar.
Spoon some mayonnaise onto each plate for dipping the artichoke leaves and pass the extra sauce at the table.