Preheat the oven to 350 degrees F. Liberally salt and pepper the short ribs on all sides.
In a large dutch oven set over medium high heat, add the olive oil.
Brown the short ribs on their tops and bottoms ( only two sides ) for 5 minutes. Do this in batches if your pot cannot fit all 3 lbs in at once comfortably.
Remove the meat from the pot and set it aside on a clean plate. Reduce the heat to medium. Add the diced onion, carrots, and celery. Cook 8 - 10 minutes, or until they start to soften.
Add the tomato paste and the garlic to the pot and stir to combine. Cook for 3 minutes. Stir in the flour, and cook for 1 minute, stirring often to prevent burning.
Stir in 2 cups of red wine. Cook for 5 minutes until the sauce starts to thicken.
Stir in the beef broth, bay leaves, whole thyme sprigs. Add the browned short ribs to the pot, and bring to a simmer.
Cover the pot and place in the oven on 350 F for 2 hours.
Once time is up, carefully remove the pot from the oven and remove the lid ( it will be HOT! Use an oven mitt! ) Remove the thyme springs and the bay leaves. Using two forks, shred the short ribs and stir them into the sauce.
Serve over pasta, with ½ a ball of burrata on top.