Sprinkle steaks evenly with 1/4 teaspoon salt and 1/4 teaspoon pepper; set aside.
Heat oil in a large nonstick skillet over medium-high heat. Add steaks; cook 3 to 4 minutes on each side or until desired degree of doneness. Remove steaks from pan; keep warm.
Reduce heat to medium; add shallots, garlic, and mushrooms. Sauté 2 minutes. Add wine, 1/2 cup beef broth, thyme, remaining 1/4 teaspoon salt, and remaining 1/4 teaspoon pepper. Increase heat to medium-high, and cook 7 minutes, stirring occasionally and scraping pan to loosen browned bits.
Combine cornstarch and remaining 1/2 cup beef broth in a small bowl, stirring with a whisk. Add cornstarch mixture to pan; bring to a boil. Cook 1 minute, stirring constantly. Return steaks to pan, and cook 1 minute or until thoroughly heated. Remove and discard thyme. Sprinkle with parsley.