Preheat oven to 325°F. Pat ribs dry.
Season ribs with salt and pepper. Dust lightly with flour, shaking off excess.
Heat olive oil in a Dutch oven over medium-high. Brown ribs on all sides; remove to a plate.
Lower heat to medium. Cook onion, carrots, and celery until softened, about 5 minutes.
Stir in garlic and tomato paste. Cook until the paste darkens slightly, about 1 minute.
Pour in red wine. Scrape up browned bits and simmer until reduced by half.
Add beef broth, Worcestershire, thyme, and rosemary. Bring to a gentle simmer.
Nestle ribs back in, bone-side up if possible. Liquid should come halfway up the meat.
Cover and braise in the oven until fork-tender, 2 to 2½ hours.
Transfer ribs to a platter. Skim fat, then simmer sauce to thicken to your liking.
Taste and adjust seasoning. Spoon sauce over ribs and finish with parsley.