Season and dust the beef: Pat the beef dry with paper towels. Toss with salt, pepper, and flour until lightly coated. This helps with browning and thickens the stew later.
Brown in batches: Heat 1–2 tablespoons oil in a heavy pot or Dutch oven over medium-high.
Brown the beef on 2–3 sides without crowding, about 6–8 minutes per batch. Add more oil as needed. Transfer browned beef to a plate.
Soften aromatics: Lower heat to medium.
Add the onion with a pinch of salt and cook until translucent, 4–5 minutes. Stir in garlic and tomato paste and cook 1–2 minutes until the paste darkens slightly.
Deglaze with wine: Pour in the red wine. Scrape up the browned bits from the bottom.
Simmer 3–5 minutes to reduce by about a third and cook off the alcohol edge.
Build the base: Return the beef and any juices to the pot. Add beef broth, bay leaves, and thyme. Bring to a simmer, then reduce heat to low.
Cover and cook gently for 60 minutes, stirring occasionally.
Add vegetables: Stir in carrots, potatoes, and mushrooms. Add Worcestershire sauce. Cover and simmer another 45–60 minutes, until beef is very tender and vegetables are cooked through.
Adjust thickness: If the stew is too thin, simmer uncovered 10–15 minutes to reduce.
If too thick, splash in more broth or water. Aim for a glossy, spoon-coating consistency.
Finish and season: Remove bay leaves and thyme stems. Stir in red wine vinegar if using.
Taste and adjust salt and pepper. Sprinkle with parsley before serving.