Heat 1 tablespoon of the oil in a medium skillet (ideally not nonstick) over medium-high heat. Season the beef with salt and pepper. Add the medallions to the pan and cook about 3 minutes on each side, for medium-rare, or until desired doneness. Remove beef from pan and set on plates or a platter in a warm spot.
Add the remaining 1 1/2 teaspoons oil to the skillet. Add the shiitakes and cook over medium-low heat, until soft, about 4 minutes. Add the shallots, garlic, and salt and cook until translucent, about 2 minutes. Pull the skillet from the heat, add the Cognac, and use a wooden spoon to scrape up any brown bits that cling to the pan. Return to the heat and cook until the liquid is reduced, about 1 minute. (If you are cooking over a gas flame the alcohol may flame, simply cook until the flames die down.) Add the chicken broth, and cook until saucy, about 2 minutes more. Remove from the heat, stir in the sour cream and parsley, and season with salt and pepper.
Spoon mushrooms and sauce over the medallions and serve.
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