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Preheat broiler and place an oven rack about 6 inches away from the broiler.
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Brush olive oil onto bottom and sides of an oven-safe ramekin.
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Put pesto, heavy cream, salt, pepper, and about half the Parmesan into the ramekin and whisk to combine. Add eggs and stir gently – do no break the yolks!
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Broil for 5 – 6 minutes or until the whites are set the the yolks are done to your preference.
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Serve hot with toast on the side.