Pat the steak dry. Cut against the grain into thin strips. Cut the strips crosswise so you have 1-inch x 2-inch pieces the beef (they will look rather large, but this size stays more tender). Place in a bowl and top with the salt, pepper, garlic powder, and onion powder. Stir to evenly coat.

In a Dutch oven or similar large, deep pot, heat the oil over medium-high heat. Once the oil is hot and shimmering, add the beef in a single layer. Let cook undisturbed for 3 minutes. Stir and spread back into an even layer. Turn the pieces as needed so that they cook on both sides. Let cook on the other side until the beef is browned all over, about 2 minutes more. Transfer to a plate and cover to keep warm.

Sprinkle the flour over the top of the mushrooms. Stir continually, until all of the white bits of the flour disappear. Splash in about one-third of the broth. Stir to scrape off any bits that have stuck to the bottom of the pot.

Add the rest of the beef broth and increase the heat to a simmer. Add the egg noodles and cover the pan. Bring the liquid to a boil, then immediately remove the lid and stir the pan. Re-cover, then reduce the heat to a low simmer. Let simmer until the noodles are al dente and most of the liquid is absorbed, about 7 minutes, stirring the noodles and recovering the pot every few minutes. If at any point the liquid drops below a gentle simmer, increase the heat slightly.

While the noodles cook, place the Greek yogurt in a medium bowl. Scoop out a few spoonfuls of the simmering broth and stir it in with the Greek yogurt. Stir in the Worcestershire and mustard. Set aside (this step deters curdling).

Once the noodles are cooked, uncover the pot and add the cornstarch slurry. Stir and let simmer until the broth at the bottom of the pot thickens slightly, about 1 minute. Remove from the heat and let cool 1 minute.

Stir in the beef along with any juices that have collected on the plate, thyme, and the Greek yogurt mixture. Taste and adjust seasonings as desired (we usually add a pinch or two of additional pepper). Let rest a few minutes, then serve hot with additional fresh thyme sprinkled on top.