Heat the oil in a sauté pan over medium-high heat. Season the medallions with salt and pepper and sear on both sides for 30 seconds. Reduce the heat to low and add the mushrooms around the beef. Cook for 3 minutes, or until the mushrooms start to give up their liquid, then add the shallots. Salt the mushrooms lightly.
Meanwhile, heat the polenta cakes by sautéing them gently in butter or oil.
Continue to cook the beef, turning once, for another 5 to 8 minutes, until medium-rare. Put the medallions on a plate to rest and keep them warm with the mushrooms. Pour the fat out of the pan and deglaze with the meat jus.
To serve, put a hot polenta cake in the center of each of 4 hot plates. Spoon the mushroom sauce around the outer edge of the flat part of the plate. Put the cabbage or whatever vegetable garnish you please on top of the polenta and around the plate. Spoon the mushrooms on top of the vegetable and around the base of the polenta cakes. Slice the meat and arrange on top of the mushrooms. Finally, spoon the meat sauce over the sliced beef and present at once.
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