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Separate 4 of the yolks from whites.
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In a mixing bowl, combine the egg whites and four whole eggs. Beat well.
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Add 1 tablespoon oil to a skillet on medium high heat.
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Add in the corned beef and char on all sides. Remove from pan and set aside.
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Add in the rye bread and crisp on all sides.
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Add back in the corned beef and add in the milk.
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After the milk is absorbed, add in the second tablespoon of oil.
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Pour in the beaten eggs.
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Add the salt and pepper and 3 broken slices of the cheese.
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Cook for two minutes on stovetop.
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Place in a 350 degree oven and back for 15 minutes until it just sets.
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Remove from the oven and top with the remaining cheese.
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Place back in the oven and cook for 3 more minutes.
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Serve and enjoy.