Preheat the oven to 160 ºC. Season the ribs with salt and pepper and heat the extra virgin olive oil on the stove in an ovenproof casserole dish.
2.
Brown the ribs over medium-high heat on all sides. Remove the ribs and set them aside.
3.
Add the chopped onion and sliced carrot and cook for 5 minutes. Add the chopped garlic and tomato paste and cook for a couple more minutes.
4.
Pour in the red wine and cook for 3-4 minutes, scraping the bottom of the pan to release the drippings.
5.
Add the broth, 2 tablespoons of balsamic vinegar, and the thyme. Add the ribs back to the casserole dish, cover and bake in the oven for about 2 ½ hours, until the meat is very tender.
6.
Remove the ribs from the casserole dish. If the sauce is too thin, cook it for a few minutes over medium heat to reduce it. Add the remaining tablespoon of balsamic vinegar and stir.
7.
Serve the ribs with the sauce poured over the top.