Preheat the oven to 325° F. Season short ribs generously on all sides with salt and pepper.

Spray a large skillet with oil and set over medium-high heat. Add the short ribs and brown on all sides, about 10 minutes. Transfer the browned ribs to an oven-safe 11-inch baking dish and set aside. Leave the rendered short ribs fat in the skillet.

Over medium-high heat, add onions to the skillet. Cook, stirring, until the onions are well browned, about 6 minutes. Add tomato paste and flour; cook and stir for 2 minutes more. Stir in the wine (or red wine vinegar) to deglaze the skillet, and continue cooking another minute to reduce the liquid a bit. Stir in 2 cups of the beef broth and allow the liquids to boil and reduce for a few minutes until slightly thickened.

Place the pan of ribs on a baking sheet and add the carrots, celery, and garlic evenly over the top. Add the fresh herbs, and pour the cooking liquids and onions from the skillet over the top. Spread everything out evenly, and cover very tightly with heavy duty foil.

Bake in the preheated 325°F oven until the meat is tender, but not falling off the bone, 3 to 3 1/2 hours. Mine were perfect after 3 hours, but ovens vary. Remove the pan from the oven.

Carefully remove the ribs and set aside. Discard the herbs. With slotted spoon, remove remaining solids from the pan. Place in a blender (or use an immersion blender) with 1/2 cup of pan juices, and blend until smooth.

Add remaining beef broth to the pan, and stir to loosen any bits from the pan. Transfer short ribs back in, spacing evenly, and baste the tops thoroughly with the cooking liquids.

Bake, uncovered, in the preheated 325°F oven until meat is heated through and very tender, 45 minutes to an hour. If the ribs are getting too dark, cover with foil to finish baking. (While baking, prepare your favorite mashed potatoes; I prefer homemade.) Remove ribs from oven and taste broth for seasoning. Adjust with salt if needed.

To serve, plate a serving of mashed potatoes, top with short rib(s), and spoon the sauce over all. You can garnish with some additional fresh thyme leaves sprinkled over the top.