How to Make It
Brush the steak with olive oil and season it with salt and pepper. Heat a large cast-iron skillet until nearly smoking. Add 1 tablespoon of the olive oil, then add the steak and cook over high heat, turning once, until well browned outside and medium-rare within, about 12 minutes. Transfer the steak to a plate, cover loosely with foil and let rest.
Meanwhile, in a large skillet, heat the remaining 2 tablespoons of oil with 1 tablespoon of the butter. Add the mushrooms, season with salt and pepper and cook over moderate heat, stirring occasionally, until beginning to brown, about 6 minutes. Add the sliced shallots and cook, stirring, until softened but not browned, about 4 minutes longer. Add the red wine vinegar and cook until evaporated. Add the wine and cook until nearly evaporated, about 5 minutes. Stir in the chicken stock and the remaining 1 tablespoon of butter.
Slice the steak in half lengthwise, cutting on either side of the sinew that runs down the center. Thinly slice the steak and transfer to plates. Add the parsley and any accumulated meat juices to the mushrooms. Spoon the sauce over the steak and serve.