Pat beef dry. Season with salt and pepper, then toss with flour to lightly coat.
Heat olive oil and 1 tbsp butter in a large skillet over medium-high heat.
Brown beef in two batches, 3–4 minutes per side. Transfer to a plate.
Lower heat to medium. Melt remaining butter. Cook onion 3 minutes, then add mushrooms and sauté until browned.
Stir in garlic for 30 seconds, then mix in tomato paste until it darkens slightly.
Pour in broth and scrape up browned bits. Add Worcestershire, soy sauce, and thyme; bring to a simmer.
Return beef and juices. Cover and simmer gently 25–30 minutes, until tender.
Whisk cornstarch with cold water. Stir into the pan and simmer 2–3 minutes until the gravy thickens. Adjust seasoning.
Meanwhile, boil egg noodles in salted water until just tender. Drain well.
Serve beef and gravy over noodles. Finish with chopped parsley.