Trim the rib-eye steak and pound it to about 1/3-inch thickness. Slice into strips and season both sides generously with kosher salt and freshly cracked black pepper. Season just before cooking to avoid drawing out moisture.

Heat 1 tablespoon of oil in a large skillet over high heat until shimmering. Working in two batches, sear half the beef strips for about 30 seconds per side until deeply browned but not cooked through. Transfer to a plate. Add the remaining tablespoon of oil and repeat with the remaining beef. Set all seared beef aside.

Reduce heat to medium and add the butter to the same skillet. Once melted, add the sliced onion and cook for about 1 minute until softened. Add the mushrooms and cook for about 4 minutes, stirring occasionally, until golden brown. Let them sit undisturbed for 1 to 2 minutes at a time to pick up color.

Sprinkle the flour over the onion and mushroom mixture. Stir well and cook for 1 minute to eliminate the raw flour taste. Pour in 1/2 cup of the beef broth, scraping up any browned bits from the bottom of the pan. Once thickened, add the remaining 1 and 1/2 cups of broth along with the Dijon mustard. Bring to a simmer and cook for 5 minutes until slightly reduced.

Remove the skillet completely from the heat. Stir in the sour cream until the sauce is silky and fully combined. Removing from heat before adding the sour cream prevents curdling.

Return the seared beef strips and any accumulated resting juices to the skillet. Set over low heat and stir gently for about 1 minute, just until the beef is warmed through. Do not cook longer or the beef will toughen.

Serve immediately over buttered egg noodles or tagliatelle and garnish with chopped fresh chives.