Season the short ribs with salt and pepper. Preheat oil in a cast-iron Dutch oven or heavy bottomed pot over moderately high heat. Sear the short ribs on all sides, then remove from the pot and set aside to be reintroduced later.

Reduce to moderate heat, then add the carrot, onion, and celery to the pot. Stirring occasionally, sauté until slightly golden brown and the carrots are tender. Deglaze the pot with red wine and simmer until almost dry. Add the tomato puree, bay leaves, thyme, rosemary, and garlic. Simmer for an additional 5 minutes to darken and reduce slightly. Stir in the beef stock, bring to a simmer, and submerge the seared short ribs in the sauce. Cover with a lid and simmer for 4 hours. Add additional stock as needed to maintain moisture while braising and prevent scorching. Serve warm over polenta.