Preheat your oven to 325°F (163°C).
Season the short ribs generously with salt and pepper on all sides.
Heat the olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Sear the short ribs in batches until they are browned on all sides, about 4-5 minutes per side. Remove the browned ribs and set them aside on a plate.
In the same pot, add the chopped onion, carrots, and celery. Cook, stirring occasionally, until the vegetables are softened, about 5 minutes. Add the minced garlic and cook for an additional 1-2 minutes until fragrant.
Pour in the red wine, scraping the bottom of the pot with a wooden spoon to loosen any browned bits (fond). Let the wine simmer for a few minutes until it has reduced slightly.
Stir in the beef broth, thyme sprigs, bay leaves, and tomato paste. Bring the mixture to a simmer.
Return the browned short ribs to the pot, nestling them into the liquid. Cover the pot with a lid and transfer it to the preheated oven. Braise the short ribs for 2.5 to 3 hours, or until the meat is tender and falling off the bone.
Once the short ribs are done, carefully remove them from the pot. Discard the thyme sprigs and bay leaves. Serve the short ribs hot, garnished with chopped fresh parsley if desired. Enjoy!