01 - Preheat the oven to 325°F. Season short ribs generously with salt and black pepper.
02 - Heat olive oil in a large Dutch oven over medium-high heat. Brown short ribs on all sides, about 8–10 minutes. Remove and set aside.
03 - Add diced onion, carrots, and celery to the pot. Sauté until softened, 5–7 minutes. Stir in minced garlic and cook for 1 minute.
04 - Incorporate tomato paste and cook for 2 minutes. Pour in red wine, scraping any browned bits from the bottom. Simmer until reduced slightly, approximately 5 minutes.
05 - Add beef broth, rosemary, thyme, and bay leaves. Return short ribs with juices to the pot and bring to a simmer. Cover and transfer to the oven to braise for 2½ to 3 hours, until meat is tender and falling off the bone.
06 - Thirty minutes before ribs finish, bring water to a boil in a medium saucepan. Gradually whisk in polenta, reduce heat to low, and cook, stirring frequently, until thick and creamy, about 20–25 minutes.
07 - Stir milk, butter, and Parmesan into the polenta. Season with salt and pepper. Keep warm on low heat, adding additional milk if needed for desired creaminess.
08 - Remove short ribs from braising liquid, discard herb sprigs and bay leaves. Skim fat from sauce and simmer to desired thickness if needed.
09 - Serve creamy polenta topped with braised short ribs and spoon braising sauce over the top.