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1
Fill a 2- to 3-quart saucepan three-fourths full of cold water, then whisk in flour, oil, salt, and juice of 1 lemon half. (Do not heat.)
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2
Cut off stem of 1 artichoke, then trim 1/4 inch from end of stem to expose core. Trim sides of stem down to pale core, then rub with remaining lemon half. Drop stem into water in pan.
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3
Cut off top 2 inches of leaves from same artichoke with a serrated knife. Bend back outer leaves until they snap off close to base, then discard several more layers of leaves until exposed leaves are pale yellow. Trim dark green fibrous parts from base and side of artichoke with a sharp paring knife, then cut remaining leaves flush with top of artichoke bottom. Rub artichoke bottom all over with same lemon half, then drop artichoke bottom into water in pan, putting a sieve or small lid directly on top of artichoke to keep submerged. Prepare other artichoke in same manner.
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4
Bring water to a boil, then reduce heat and simmer artichokes, uncovered, keeping them submerged, until just tender, 10 to 15 minutes for stems and 15 to 20 minutes for bottoms. Transfer as cooked with tongs to a cutting board.
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5
When artichokes are cool enough to handle, remove pointed inner leaves and fuzzy chokes with a melon-ball cutter or with a small spoon.
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6
Artichokes can be cooked 1 day ahead and transferred to a bowl with some cooking liquid and 1 cup cold water (to stop the cooking). Cool, then chill in cooled liquid, covered. Drain artichokes before using.
