Pat oxtails dry. Season all over with salt and pepper, then toss lightly in the flour.
Heat oil in a heavy pot over medium-high. Brown oxtails on all sides in batches. Set aside.
Lower heat to medium. Cook onion, carrots, and celery until softened, about 6–8 minutes.
Stir in garlic and tomato paste. Cook until the paste darkens and smells sweet, 2 minutes.
Pour in red wine. Scrape up browned bits and simmer 2–3 minutes to reduce slightly.
Return oxtails to the pot. Add beef stock, diced tomatoes, Worcestershire, thyme, and rosemary. Bring to a simmer.
Cover and braise on low heat until oxtails are very tender, about 2 hours 15 minutes.
Stir in potatoes. Continue simmering covered until potatoes are tender and meat is falling off the bone, 40–50 minutes.
Skim excess fat. If you want it thicker, whisk cornstarch with water and stir in. Simmer 2 minutes.
Taste and adjust salt and pepper. Let rest 5 minutes, then sprinkle with parsley and serve.