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Remove all visible fat and tough sinew from the pork tenderloin. Cut the meat crosswise into 1-1 1/2 inch medallions.
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Place each medallion, cut sie up, on a cutting board between two pieces of plastic wrap. Flatten with broad side of a wide knife or rolling pin to a thickness of 1/4 inch. Sprinkle with salt and pepper.
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Heat oil and 1 tablespoon of the butter in a large non-stick skillet. Saute the medallions 3-4 minutes on each side. Remove to a platter and keep warm.
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Let skillet cool slightly. Add shallots to oil and butter mixture remaining in skillet and cook 1 minute. Add mushrooms and cook 1 minute. Add sherry, chicken stock and vinegar. Bring mixture to a boil and boil rapidly until liquid is reduced by half. Turn off heat.
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Cut remaining tablespoon of butter into small chunks and stir into sauce. Adjust seasoning to taste with salt and pepper or more vinegar if desired.
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Serve pork medallions covered in mushroom sauce.