Preheat oven to 325° F.

Generously season the short ribs with salt and pepper. Heat the olive oil in a large Dutch oven over medium-high heat. Add the short ribs to the pot and brown them on all sides, 30 seconds to 1 minute per side. Remove ribs to a clean plate.

Add the onion and carrot to the pot and sauté until they start to soften, about 3 minutes.

Reduce heat to medium. Add the garlic, flour and tomato paste. Cook, stirring constantly, for 1 minute.

Pour in the red wine and stir, scraping up any browned bits from the bottom of the pot. Stir in the beef stock, balsamic vinegar, salt and pepper and bring to a simmer. Add the short ribs back to the pot, spoon some of the sauce over the top of the ribs, then add the fresh thyme sprigs.

Cover the pot and bake in the preheated oven for 2 - 2 ½ hours, until the meat is fall-apart tender. Remove from the oven and let rest with the lid on for 10-15 minutes. Remove and discard the thyme stems. Skim any excess fat off of the top of the sauce, as needed. Taste and add more salt and pepper if needed.

Serve ribs over mashed potatoes or polenta with the sauce spooned over the top.