Cook noodles according to package directions, omitting salt and fat, then drain.
While the noodles cook, heat a large nonstick skillet over medium-high heat. Spread the olive oil around the pan or coat it with cooking spray. Sauté the steak pieces, browning on all sides. Remove from the pan and cover.
Melt the butter in the pan over medium-high heat. Add the shallots and mushrooms, and sauté 4 minutes. Add the garlic and sauté 30 seconds. Stir in the Worcestershire sauce or soy sauce. Sprinkle the cornstarch over the mushroom mixture and cook for 1 minute stirring constantly. Gradually add the broth, stirring constantly. Add pepper, salt, and thyme sprigs. Bring to a boil, then cook until thickened, about 2 more minutes. Return the beef to pan and until thoroughly heated, about 1 more minute. Discard the thyme sprigs. Serve with the noodles, and garnish with thyme leaves, if desired.