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1
Discard any discolored outer stalks and small leaves from cardoons. Trim base, tips, and outermost stalks, removing strings from stalks with a vegetable peeler (as for celery), then cut cardoons crosswise into 2-inch pieces.
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2
Soak cardoons in 2 quarts water with 1 tablespoon salt in a large bowl, chilled, at least 8 hours.
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3
Drain cardoons. Transfer to a 6-quart pot, then generously cover with cold water and add 2 tablespoons salt. Bring to a boil, then simmer, uncovered, until tender when pierced with a sharp knife, 20 to 25 minutes. Drain on several layers of paper towels and cool 5 minutes.
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4
Heat about 1 1/2 inches oil to 360u00b0F in a 4- to 5-quart heavy pot over medium heat.
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5
Whisk together flour and 1/4 teaspoon pepper in a shallow bowl. Whisk together eggs, water, and cheese in another shallow bowl.
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6
Toss one fifth of cardoons (all at once) with flour, shaking off excess, then transfer to egg mixture and turn with a fork to coat. Lift out coated cardoons 2 at a time, letting excess drip off, then carefully drop into hot oil. When all of batch has been added, fry, turning occasionally, until golden, 2 to 4 minutes. Transfer with a slotted spoon to fresh paper towels to drain.
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7
Coat and fry remaining cardoons in 4 batches. (Return oil to 360u00b0F between batches.) Season with salt.
