Pat steak strips completely dry with paper towels. Season generously with 1/2 tsp kosher salt and 1/4 tsp cracked black pepper.

Heat 1 tbsp olive oil and 1 tbsp butter in a large heavy cast-iron skillet over high heat until shimmering. Add steak strips in an uncrowded single layer and sear undisturbed for 60-90 seconds per side until deeply browned but tender medium-rare. Transfer seared beef immediately to a clean plate.

Reduce heat to medium. Melt remaining 3 tbsp butter in the same skillet. Add sliced cremini mushrooms and sauté for 5-6 minutes until deeply caramelized and tender.

Add minced shallot and garlic; cook for 1-2 minutes until aromatic. Sprinkle 2 tbsp flour over mushrooms and stir continuously for 1 minute to cook out raw flour taste.

Slowly pour in beef bone broth while whisking continuously to deglaze the skillet, scraping up all browned fond from the pan bottom. Whisk in Dijon mustard, Worcestershire sauce, and fresh thyme. Bring sauce to a gentle simmer for 3-4 minutes until smooth and thickened.

Remove skillet from heat. Stir in room-temperature sour cream until silky and fully integrated. Return seared steak along with any resting juices into the skillet, stirring gently over low heat for 1 minute just to warm through. Do not boil once sour cream is added.

Divide warm buttered egg noodles among shallow bowls. Spoon generous ladles of beef stroganoff and mushroom gravy over top. Garnish with chopped Italian parsley, fresh dill, and cracked black pepper. Serve immediately.