Take the steaks out of the refrigerator about half an hour before cooking them.
In an ovenproof heavy skillet or cast iron pan, melt one tablespoon butter over medium high heat. Add the sliced mushrooms saute until they've given up their liquid and started to brown. Transfer the mushrooms to a bowl and set aside. (Can be made ahead).
Season both sides of the steaks with salt and pepper. In the same skillet, heat the remaining tablespoon of butter over high heat until foamy and add the steaks to the skillet. Sear the meat on one side for about 2 minutes. Use a pair of tongs to flip the steaks. Cook for an additional 1 1/2 to 2 minutes (for medium rare), then transfer to the hot oven and cook for 2-3 more minutes for medium rare. Remove the skillet from the oven and transfer the steaks to a cutting board or serving platter to rest for five minutes before serving.
While the steak rests, heat the bordelaise sauce and stir in the mushrooms. Spoon the sauce over the steaks and serve.