Fill a medium bowl with cold water. Squeeze the juice of two lemons into the water and add the lemon halves.
Trim the artichoke stems to 1 inch, and peel off dark-green outer layer. Trim 2 1/2 to 3 inches from top of each artichoke, and pull off tough outer leaves until tender yellow ones appear. Using a spoon, scoop out purple choke; discard. Slice the artichokes lengthwise, about 1/3 inch thick, and place in lemon water.
In a large nonstick skillet, combine oil and juice of remaining lemon. Drain artichokes; add to skillet with garlic, salt, peppercorns, and 3 cups water. Arrange all but 1 sprig tarragon on top of artichokes; bring to a boil. Boil until a trace of water remains, about 15 minutes. Discard tarragon. Reduce heat to medium; continue cooking until artichokes are crisp and golden brown, about 5 minutes on each side. Meanwhile, chop leaves of remaining tarragon sprig.
Transfer artichokes to a serving dish; garnish with chopped tarragon.
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