Preparation

• Pat the steaks dry and season with salt and pepper. In a heavy-duty 12-inch skillet (preferably cast iron), heat 2 Tbs. of the olive oil over high heat until shimmering hot. Cook the steaks in a single layer, flipping with tongs halfway through, until an instant-read thermometer inserted in the thickest part of the steak registers 130°F for medium rare, 5 to 7 minutes total (if necessary, lower the heat to medium high to finish cooking the thicker pieces). Transfer to a plate and let rest, loosely covered with foil, while making the sauce.
• Heat 2 Tbs. of the olive oil in the skillet over medium-high heat until shimmering hot. Add the mushrooms and a generous pinch of salt and cook, stirring occasionally with a wooden spatula, until golden-brown, 6 to 8 minutes. Transfer to a bowl and keep warm.
• Lower the heat to medium, add the remaining 1 Tbs. olive oil, the shallot, and thyme and cook, stirring, until the shallot is slightly browned, about 1 minute. Add the wine and cook, stirring and scraping the bottom of the pan to dissolve any browned bits, until the liquid has almost evaporated, about 1 minute. Add the chicken broth. Raise the heat to high and boil, adding any juice that has accumulated from the steak and mushrooms, until the sauce is reduced to about 1/3 cup, about 7 minutes.
• Remove the pan from the heat and whisk in the butter. Stir in the mushrooms and season the sauce to taste with salt and pepper.
• Thinly slice the steaks diagonally across the grain, if you like, and serve topped with the mushroom sauce.