Add the oil to a large cast-iron skillet over medium-high heat. Heat until the oil is very hot. Season the steaks with salt and pepper. Add the steaks to the skillet and sear the steak on each side for 4 minutes for medium. Remove the steaks from the skillet and cover with foil.

Lower the heat to medium and add the mushrooms, shallot, and thyme to the pan and sauté until the mushrooms begin to brown and soften, about 5 minutes. You may need to add a bit more oil to the pan. Add the red wine and bring to a boil to deglaze the pan, about 2 minutes.

Let the liquid reduce by half, 7 to 8 minutes. Remove from the heat and swirl in 3 tablespoons butter to finish the sauce. Serve the steak with mushroom red wine sauce drizzled over the top.