Bring a large stockpot of generously salted water to a rolling boil. Add the wide egg noodles and cook according to the package directions until they reach an al dente texture.
Drain the cooked noodles thoroughly and set them aside until needed.
While the noodle water is heating or the noodles are cooking, place a large sauté pan over medium heat and melt 2 tablespoons of the butter.
Arrange the sliced flank steak in a single layer and season it well with fine sea salt and coarse black pepper. Leave the meat undisturbed for approximately 3 minutes so it can develop a browned exterior.
Turn the steak pieces and continue cooking for another 2–3 minutes, or until browned on the second side. Transfer the beef to a clean plate with a slotted spoon and reserve it for later.
If the pan cannot comfortably accommodate all of the steak in one layer, brown the meat in two batches, using approximately 1 tablespoon of butter for each batch.
Add the remaining 2 tablespoons of butter to the same sauté pan and melt it over medium heat.
Add the sliced onion and cook for approximately 3 minutes, allowing it to begin softening.
Stir in the sliced mushrooms and continue cooking for 5–7 minutes, stirring from time to time, until the mushrooms have browned and the onion is tender.
Add the minced garlic and cook for an additional minute. As the vegetables cook, gently loosen any browned bits remaining on the bottom of the pan and incorporate them into the mixture.
In a separate bowl, thoroughly whisk together the beef stock, Worcestershire sauce, and all-purpose flour until the mixture is completely smooth and free of flour lumps.
Pour the stock mixture into the pan containing the mushrooms and onions. Bring the sauce to a gentle simmer, stirring occasionally and scraping the bottom of the pan to incorporate any remaining browned residue.
Continue simmering for approximately 5 minutes, or until the sauce has thickened to the desired consistency.
Return the browned steak and any accumulated juices to the pan. Allow the stroganoff to simmer gently for 2–3 minutes, just until the beef is heated through.
Taste the finished sauce and season with additional fine sea salt and coarse black pepper as necessary. Remove the pan from the heat and allow the stroganoff to rest briefly before serving.
Combine the cooked egg noodles with the beef and mushroom sauce, tossing gently until the noodles are evenly coated. Alternatively, portion the noodles onto individual plates and spoon the stroganoff over the top.
Finish each serving with chopped fresh parsley and an additional sprinkling of coarse black pepper, if desired.