Preheat the oven to 350ºF.
Season ribs with salt, pepper, and dredge in ¼ cup flour (shake off excess). Heat oil in a large skillet or Dutch oven over medium-high heat. Brown the ribs on all sides, then remove and set aside.
Sauté onions, carrots, celery, and garlic 4-6 minutes, or until vegetables are tender.
Add ¼ cup flour and tomato paste, cook 1 minute. Add a splash of the beef stock if you need a little moisture.
Pour in wine and beef stock. Return the short ribs and any juices. Scrape up any solid bits from the bottom or the pan.
Top with fresh herbs. Bring to a boil, cover, and transfer to the oven. Bake 3 hours. Remove herb stems from the top.
Serve the ribs over mashed potatoes or another side item, and top with gravy.