Preheat the oven to 325°F. Pat the short ribs dry, then season generously with salt and pepper on all sides.

Heat the olive oil in a Dutch oven over medium-high heat. Sear the ribs in batches until browned on all sides, then remove them to a plate.

Lower the heat to medium and add the onion and carrots to the pot. Cook for 5 minutes until softened. Stir in the garlic and tomato paste and cook for 1 minute more.

Pour in the red wine and scrape the bottom of the pot to release any browned bits. Let the wine simmer for 3 minutes to reduce slightly.

Add the beef broth, thyme sprigs, and bay leaves. Return the short ribs to the pot, cover, and transfer to the oven. Braise for 2.5 to 3 hours until the meat is very tender.

About 30 minutes before the ribs are done, make the polenta. Bring the milk to a simmer in a large saucepan. Slowly whisk in the polenta and a pinch of salt. Cook, stirring often, for 20 minutes until thick and creamy.

Remove the polenta from heat and stir in the butter and Parmesan. Taste and adjust seasoning if needed.

Spoon the creamy polenta into bowls, top with short ribs and some of the braising sauce, then finish with chopped parsley.