Pat the short ribs dry and season them all over with the salt and pepper. Heat the olive oil in a Dutch oven over medium-high heat and brown the ribs on all sides, working in batches if needed. Remove the ribs and set them aside.

Lower the heat to medium and add the onion and carrots to the same pot. Cook for 5 minutes until the vegetables soften. Stir in the garlic and cook for 1 minute more.

Pour in the red wine and beef broth. Add the thyme and bay leaves. Return the short ribs to the pot and bring the liquid to a simmer.

Cover the pot and transfer it to a 325°F oven. Cook for 2.5 to 3 hours until the meat is very tender and pulls away from the bone easily.

While the ribs finish, bring the milk to a gentle simmer in a large saucepan. Whisk in the polenta slowly and cook, stirring often, for 20 to 25 minutes until thick and creamy.

Stir the butter and Parmesan into the polenta until fully melted. Season with a pinch of salt if needed. Serve the short ribs and some of the wine sauce over scoops of the polenta.