01 - Preheat oven to 325°F. Generously season the short ribs with salt and black pepper.
02 - Heat olive oil in a large Dutch oven over medium-high heat. Sear the short ribs on all sides until browned, about 8 to 10 minutes. Remove and set aside.
03 - Add diced onion, carrots, and celery to the pot and cook until softened, 5 to 7 minutes. Stir in minced garlic and cook for 1 additional minute.
04 - Incorporate tomato paste and cook for 2 minutes. Pour in dry red wine, scraping the bottom of the pot to release browned bits. Simmer until slightly reduced, about 5 minutes.
05 - Stir in beef broth, fresh rosemary, thyme, and bay leaves. Return short ribs to the pot along with any accumulated juices. Bring to a simmer.
06 - Cover the pot and transfer to the preheated oven. Braise the meat for 2½ to 3 hours, until tender and falling off the bone.
07 - Approximately 30 minutes before the ribs finish, bring water to a boil in a medium saucepan. Gradually whisk in the polenta. Reduce heat to low and cook, stirring frequently, until thick and creamy, about 20 to 25 minutes.
08 - Stir in whole milk, butter, and grated Parmesan. Season with salt and freshly ground black pepper. Keep warm over low heat, adding more milk as needed to maintain desired creaminess.
09 - Remove short ribs from the braising liquid. Discard rosemary, thyme, and bay leaves. Skim excess fat and reduce sauce over medium heat if a thicker consistency is preferred.
10 - Spoon creamy polenta into serving bowls. Top with braised short ribs and a generous ladle of the braising sauce.