Pound the rib-eye to ¾ cm thickness using a meat mallet. Slice into finger-width strips across the grain, pat completely dry with paper towels, then season generously with salt and pepper. Let sit for 10 minutes at room temperature so the meat cooks evenly.

Heat 1 tablespoon oil in a large skillet over high heat until shimmering. Lay half the beef strips flat without crowding. Leave untouched for 30 seconds to develop a golden crust. Flip and cook 30 seconds more until beef reaches 54-57°C (130-135°F) for medium-rare. The strips should be pink inside with a caramelized exterior. Transfer to a plate. Add remaining oil and repeat with remaining beef.

Lower heat to medium-high. Melt butter, add onions, and cook for 1 minute until softened and fragrant. Scatter mushrooms in a single layer and resist the urge to stir for 2 minutes. The mushrooms are ready when they've released their moisture and turned deep golden with slightly crispy edges. Stir and cook 2 minutes more. Season lightly with salt.

Sprinkle flour over the vegetables and stir for 1 minute to eliminate the raw flour taste. The mixture will look dry and pasty at first, which is exactly what you want.

Pour in ½ cup broth while scraping up browned bits from the pan bottom with a wooden spoon. When smooth, whisk in remaining broth and Dijon mustard. Simmer for 5 minutes until sauce coats the back of a spoon and reduces slightly.

Remove pan from heat completely. Wait 30 seconds for the pan to cool slightly, then stir in sour cream until the sauce turns velvety and uniform. The residual heat will warm it without curdling. Never let sour cream boil or it will separate.

Slide the seared beef and accumulated juices back into the pan. Set heat to low and warm for 1 minute without additional cooking. Spoon over buttered noodles, garnish with chives, and finish with black pepper.