1Remove the steaks from the refrigerator 30 minutes before cooking to come to room temperature.
2While the steaks come to room temperature, in a frying pan, melt 2 tablespoons of the butter. Add the mushrooms and shallots and a sprinkle of salt and sauté until browned and tender, about 7 minutes. Set aside.
3Preheat the oven to 425°F. Pat the filets dry with paper towels and season with plenty of salt and pepper. Heat a large cast-iron frying pan over high heat for about 5 minutes.
4When the pan is very hot, add the olive oil and then the steaks; sear for about 4 minutes on one side. Turn and sear for another 2 minutes, then transfer to the oven.
5Roast the filets in the oven until cooked to your desired doneness, about 5 minutes depending on the thickness of the steak (rare = an internal temp of 120°F; medium-rare = 125°F). Transfer the steaks to a platter, cover tightly with aluminum foil, and let rest for 5 to 10 minutes while you finish the sauce.
6While the steaks are resting, return the frying pan with the mushroom mixture to the stovetop. Add the red wine and simmer until reduced by half. Add the remaining butter. Serve the filets with the mushroom sauce over the top.