Pat ribs dry with paper towel, and season with salt and pepper
Dredge ribs in flour, shaking off excess flour
Heat olive oil in large dutch oven, and brown ribs on all sides, working in batches if necessary. Place on plate, and cover with foil to keep warm
Cook carrots, celery and onion until soft, then add garlic, and cook until fragrant
Stir in tomato paste, then stir in red wine, and deglaze pot using a wooden spoon or spatula to scrape up any browned bits sticking to pot
Place ribs back into pot, and stir in beef broth. Ribs should be mostly submerged. You can add another ½ cup broth if needed. Add thyme on top
Bring to a simmer on the stove
Preheat oven to 325℉
Cover with lid, and cook short ribs in oven for 2 ½ to 3 hours or until fork tender and falling off the bone, checking occasionally to make sure ribs aren't boiling
Spoon sauce over ribs or remove ribs to a platter, strain out the veggies, and reduce sauce on the stove until thickened, then serve