Remove all visible fat and tough sinew from the pork tenderloin. Cut the meat crosswise into 1-1 1/2 inch medallions.
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.
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.
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.
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.