Preheat a cast iron grill or outdoor grill.
Season the short ribs with salt and pepper, drizzle with a little extra-virgin olive oil, and brown on all sides.
Place the onion, garlic, celery, carrot, and tomato into a food processor and blend until you reach a consistent, smooth pulp.
Take a large Dutch oven and place over medium-high heat. Add a 3-count of extra-virgin olive oil and add the thyme to infuse the oil. Next add the vegetable pulp, season with salt and pepper, to taste, and cook for about 10 minutes. Pour in the red wine and stock and bring it to a boil. Using tongs take the ribs and nestle them into the braising mix; the liquid should just about cover the meat. Place the lid loosely on top, reduce heat to a simmer and cook until the meat is very tender, approximately 2 1/2 to 3 hours.
When the ribs are about finished, remove about 1 to 2 cups of liquid and strain into a small saucepan over medium-high heat. Heat the sauce until slightly reduced and thickened, about 5 minutes.