Place a large skillet over medium-high heat with 2 turns of the pan of EVOO, about 2 tablespoons. Season the steaks with salt and pepper and sear in the pan (working in batches if need be) until the steaks have a nice crust on the outside, about 3 minutes per side.
Remove the cooked steaks from the skillet and reserve warm on a plate. Return the skillet to medium-high heat and add 1 turn of the pan of EVOO, about 1 tablespoon. Add the mushrooms to the pan and cook until they start to turn golden brown, 4-5 minutes.
Add the onion and garlic to the pan, and continue cooking until the onions are tender, 4-5 minutes. Add the red wine and beef stock to the pan, season with salt and pepper, and cook down until the liquid reduces by about half. Remove the pan from the heat and add the butter, stirring to melt it.
Serve the steaks with some of the mushroom and red wine sauce and a fresh green salad alongside.