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1
Soak sweetbreads in a large bowl of ice water in the refrigerator, changing water occasionally (2 or 3 times), at least 8 hours.
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2
Drain sweetbreads and transfer to a 4-quart heavy saucepan. Cover with cold water by 1 inch and add 1 teaspoon salt. Bring to a boil, then reduce heat and simmer, uncovered, until sweetbreads plump and feel slightly firmer to the touch, about 3 minutes. Drain in a colander and transfer to an ice bath to stop cooking. Cut away any fat and pull away as much membrane and connective tissue as possible with a small paring knife, then separate with your fingers into roughly 2-inch pieces.
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3
Whisk buttermilk with 1/2 teaspoon salt in a bowl. Add sweetbreads and soak, chilled, 1 hour.
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4
About 10 minutes before sweetbreads are finished soaking in buttermilk, start heating 2 inches oil to 350u00b0F in a 5-quart wide heavy pot over medium heat. Whisk together flour, cornmeal, paprika, cayenne, and 1/2 tsp each of salt and pepper in a shallow dish.
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5
Put a metal cooling rack in a 4-sided sheet pan and preheat oven to 400u00b0F.
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6
Drain sweetbreads well, discarding buttermilk. Dredge in flour mixture, shaking off any excess, then fry in 3 batches until golden and cooked through (cut one open to test), 3 to 3 1/2 minutes, depending on size. Transfer with a slotted spoon to paper towels to drain, then season lightly with salt. Keep warm on rack in oven. (Return oil to 350deg; between batches.) Serve fried sweetbreads immediately.
