Melt the butter in a nonstick skillet over medium heat. Add the shallots and mushrooms; saute for 4 minutes. Add the wine and beef broth; cook for 5 minutes, stirring frequently. Remove the mushrooms with a slotted spoon; place in a bowl.
Increase the heat to high, cook the wine mixture until reduced to about ¼ cup (about 5 minutes). Add to the mushrooms in the bowl; set aside. Wipe the pan with a paper towel.
PREPARE THE FILETS:
Sprinkle pepper over the steaks. Melt the butter in pan over medium heat. Add the steaks; cook 3 minutes on each side. Reduce the heat to medium-low; cook 1½ minutes on each side or until desired degree of doneness. (You can use an instant read thermometer if you have one.) Place the steaks on a platter to rest; keep warm.
Combine the soy sauce and cornstarch in a small bowl; set aside. Add the wine and beef broth to the skillet; scrape the skillet to loosen any browned bits. Bring to a boil; cook 1 minute. Add the mushroom mixture, cornstarch mixture, and dried thyme; bring to a boil, and cook 1 minute, stirring constantly. Serve the sauce with the steaks. Garnish with thyme sprigs, if desired.
Notes
If preparing this recipe as GLUTEN FREE, just be sure to use brands of beef broth and soy sauce that are known to be GF.