01 - Preheat the oven to 325°F. Season short ribs generously with salt and freshly ground black pepper.
02 - Heat olive oil in a large Dutch oven over medium-high heat. Brown the short ribs on all sides, about 8 to 10 minutes. Remove and set aside.
03 - Add diced onion, carrots, and celery to the same pot. Cook for 5 to 7 minutes until softened, then add minced garlic and cook an additional minute.
04 - Stir in tomato paste and cook for 2 minutes. Pour in red wine, scraping browned bits from the bottom, and simmer until slightly reduced, about 5 minutes.
05 - Incorporate beef broth, rosemary, thyme, and bay leaves. Return short ribs with their juices to the pot and bring to a simmer.
06 - Cover and transfer the pot to the oven. Braise for 2½ to 3 hours until meat is tender and easily pulls from the bone.
07 - 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 to 25 minutes.
08 - Stir in whole milk, unsalted butter, and grated Parmesan cheese. Season with salt and pepper. Maintain over very low heat, adding more milk if necessary for desired creaminess.
09 - Remove short ribs from braising liquid. Discard herbs and bay leaves. Skim fat and simmer sauce to reduce if desired. Serve short ribs atop creamy polenta, spooning sauce over the top.