Whisk together buttermilk, eggs, salt, and pepper and pour into a 3-quart shallow dish. Add crabs and soak, covered and chilled, 1 hour. Heat enough oil to measure 2 inches in a wide 4-quart heavy pot (about 4 inches deep) to 375 degrees. Whisk together flour and cornmeal and transfer to a large sealable plastic bag. Lift 1 crab out of buttermilk, letting excess drip off, and shake in bag to coat with flour. Knock off excess flour and transfer to a tray. Repeat with remaining crabs, arranging them in 1 later as coated. Deep-fry crabs until golden brown, 3 to 5 minutes. Return oil to 375 degrees between batches. Drain crabs on paper towels.

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