Prepare the pasta and ingredients.
Cook the egg noodles or tagliatelle according to the package directions until al dente. Drain thoroughly and reserve for serving.
While the pasta water is heating, slice the cremini mushrooms to an even 1/8-inch thickness. Thinly slice the yellow onion and finely chop the chives.
Blot the rib-eye dry with paper towels, then cut the meat against the grain into slender strips.
Season and sear the steak.
Season the beef generously on both sides with kosher salt and freshly ground black pepper.
Heat 1 tablespoon of the neutral oil in a large skillet over high heat. When the oil is extremely hot and just beginning to smoke, add half of the beef in a single layer.
Sear the steak for approximately 30 seconds on each side, allowing the surface to develop a deep brown crust while the center remains rare. Transfer the first batch to a plate.
Pour the remaining tablespoon of oil into the skillet and repeat the process with the remaining beef. Keep all of the seared steak and its accumulated juices aside.
Cook the onion and mushrooms.
Leave the browned residue in the skillet and reduce the heat to medium. Add the unsalted butter and allow it to melt.
Add the sliced onion and cook for approximately 1 minute, just until it begins to soften.
Stir in the cremini mushrooms and continue cooking for about 4 minutes, stirring from time to time. Allow the mushrooms to release their liquid and develop light browning.
Prepare the sauce.
Scatter the all-purpose flour evenly over the mushroom and onion mixture. Stir continuously for 1 minute to cook the flour and remove its raw flavor.
Pour in 1/2 cup of the beef broth. Using a wooden spoon, scrape across the bottom of the skillet to loosen and incorporate the browned bits.
Add the remaining 1 1/2 cups of broth along with the Dijon mustard. Stir until the mustard is completely dispersed throughout the liquid.
Bring the mixture to a gentle simmer and cook for 5 minutes, allowing the sauce to reduce slightly and develop a thicker consistency.
Incorporate the sour cream and beef.
Take the skillet off the heat and allow the sauce to stand for approximately 30 seconds.
Stir in the room-temperature sour cream until the sauce becomes completely smooth and evenly blended.
Return the seared beef, along with any juices collected on the plate, to the skillet. Set the pan over low heat and warm the stroganoff gently for 1 minute, stirring occasionally. Avoid prolonged cooking so the beef remains tender.
Assemble and serve.
Portion the cooked egg noodles or tagliatelle among individual bowls or plates.
Spoon the beef stroganoff generously over the pasta, distributing the strips of steak, mushrooms, onions, and sauce evenly.
Finish with chopped fresh chives, if desired, and serve immediately.