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Preheat the oven to 400 degrees.
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Line a baking sheet with foil and place in oven to heat.
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Combine the salt, black pepper, and cayenne on a plate.
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Line up the spice mixture, the beaten egg whites, and the pecans in a row on the countertop for easy coating of the grouper.
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First, roll the grouper in the spice mixture, coating both sides.
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Next, dip the grouper into the egg whites, and then roll in the pecans.
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Heat the olive oil in a nonstick skillet on medium high.
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When the oil is hot, brown the grouper for 2 minutes.
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Turn and brown other side for 1 minute.
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Remove the baking tray from the oven and spray with olive oil.
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Place the grouper on the tray and return the tray to the oven for 5 minutes to finish cooking.