Season the beef strips generously with salt and black pepper on all sides. Heat olive oil and butter in a large cast-iron skillet over medium-high heat until the butter foams and the pan is very hot. Add beef strips in a single layer, working in batches if needed to avoid overcrowding. Sear for 1 to 2 minutes per side until you see a deep golden-brown crust forming, then transfer to a plate and set aside.

Reduce heat to medium and melt 1 tablespoon of butter in the same skillet. Add diced onions and cook for about 2 minutes until they start softening and turning translucent, then stir in minced garlic and sauté for another minute until fragrant. Add sliced mushrooms and cook for 5 to 6 minutes, stirring occasionally, until they release their moisture and develop rich golden-brown edges.

Sprinkle smoked paprika over the mushrooms and stir in Dijon mustard, coating everything evenly. Pour in white wine and use a wooden spoon to scrape up all those flavorful browned bits from the bottom of the pan. Let the wine simmer for 2 minutes until it reduces by half and the alcohol cooks off.

Add beef broth and Worcestershire sauce, stirring to combine. Reduce heat to low and slowly stir in the room-temperature sour cream, making sure it blends smoothly without separating. Use gentle, circular motions to incorporate it fully. Add fresh thyme and season with salt and pepper to taste, adjusting as needed.

Return the seared beef strips to the skillet along with any accumulated juices from the plate. Gently toss the beef in the sauce for 1 to 2 minutes until heated through, being careful not to overcook. Serve immediately over cooked egg noodles, rice, or mashed potatoes, garnished with chopped parsley and freshly cracked black pepper.