Preheat oven to 300°. Season short ribs heavily with salt and pepper. Heat oil in a large Dutch oven over high heat. Brown short ribs on all sides, about 8 minutes per batch. Remove the ribs and transfer to a plate. Pour off all but approximately 2 Tbsp. drippings from pot.
Add onions, garlic, carrots, and celery to pot and saute about 5 minutes. Add tomato paste; cook, stirring constantly. Stir in water, wine, then add short ribs with all the juices. Add the herbs, bring to a boil, cover, and transfer to oven.
Cook in the oven until short ribs are tender, 3–3 1/2 hours. Spoon fat from surface and discard. Transfer the ribs to a plate. Using a handheld blender puree the sauce. Reduce until desired thickness. Adjust the salt and pepper to taste.
Serve in shallow bowls over polenta or mashed potatoes with sauce spooned over.