Whisk flour, salt, pepper, and paprika in a shallow dish; set aside 1 tbsp for the gravy.
Pat steaks dry, then dredge in the seasoned flour, shaking off any excess.
Heat oil and butter in a large skillet over medium-high heat until shimmering.
Sear steaks 2–3 minutes per side until browned; transfer to a plate and keep warm.
Lower heat to medium. Add onions and cook, stirring, until golden and soft, 8–10 minutes.
Stir in garlic for 30 seconds. Sprinkle in the reserved 1 tbsp flour and cook 1 minute.
Pour in beef broth and Worcestershire, scraping up browned bits. Add thyme and bring to a simmer.
Nestle steaks and any juices into the gravy. Cover and simmer gently until tender, 20–25 minutes.
For thicker gravy, stir cornstarch with water, then whisk into skillet; simmer 1–2 minutes until glossy.
Taste and adjust seasoning. Garnish with parsley and serve hot over mashed potatoes, rice, or noodles.