Preheat the oven to 450 degrees F (230 degrees C).
Take the Filet Mignon (4) out of the refrigerator about half an hour before cooking them (filet mignon should be 1"-1 1/2" thick).
In an ovenproof heavy skillet or cast iron pan, melt the Butter (1 tablespoon) over medium high heat.
Add the Button Mushroom (8 ounce) until they've given up their liquid and start to brown. Transfer the mushrooms to a bowl and set aside. (Can be made ahead).
Season both sides of the steaks with Kosher Salt (1/2 teaspoon) and Ground Black Pepper (1/2 teaspoon).
In the same skillet, heat the Butter (1 tablespoon) 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 (1 cup) and stir in the mushrooms.
Spoon the sauce over the steaks and serve.