Heat oil in a large Dutch Oven over medium-high heat. Season short ribs with salt and pepper.
Place half the short ribs in the Dutch oven and sear on all sides Remove to a plate and sear the remaining short ribs. Place them with the other short ribs.
If necessary, add another tablespoon of oil to the Dutch oven. Add onion and cook until softened, about 5 minutes. (You may need to turn the heat down some so that they do not burn.)
Add garlic and cook 1 more minute.
Add beef broth and use a wooden spoon to scrape up any brown bits on bottom of the Dutch oven.
Add remaining ingredients and season to taste with salt and pepper. When mixture comes to a simmer, return short ribs to the Dutch oven.
Cover and cook on low heat (enough to just maintain a simmer) for about 2 hours. You will know they are done when you can shred them fairly easily.
Remove short ribs to a bowl. Turn heat up and reduce the sauce for about 20 minutes.
Shred short ribs with 2 forks and ladle sauce over them.