Preheat the oven to 350°F.
- Season the ribs with coarse salt and freshly ground black pepper.
- Heat the oil in a large Dutch oven over high heat.
- Brown the short ribs, taking care not to overcrowd your pan (overcrowding will make your ribs steam rather than sear; do in as many batches as necessary to ensure that each rib has a small amount of space around it).
- Remove the ribs and set them aside.
- Add the onions, carrots, and celery to pot and cook them for a few minutes, stirring them occasionally, until the onions are soft. Scrape the bottom to release any browned bits from searing the meat.
- Sprinkle the flour over the vegetables and add the tomato paste. Str it well and cook a few minutes longer, stirring occasionally. Return the short ribs and any accumulated juices to the pot. Pour in the wine and beef stock (you can add a small amount first then scrape up any remaining bits stuck to the bottom of the pot, then add the rest). Add all the herbs to pot along with the garlic. Bring it to a boil, cover, and transfer it to the oven.
Cook until the short ribs are tender, about 3 hours (they’re ready when they fall apart when you test them). Transfer the short ribs to a platter or a large serving bowl, and tent them with foil.Strain the sauce into a gravy strainer and remove the fat from surface. Place the gravy into a saucepan, bring it to a boil and keep it at a strong simmer until it's reduced by 1/3. Season to taste with salt and pepper.