01 - Preheat oven to 325°F. Pat beef short ribs dry and season generously with salt and pepper.
02 - Heat olive oil in a large Dutch oven over medium-high heat. Sear short ribs on all sides until deeply browned, approximately 3–4 minutes per side. Remove and set aside.
03 - Reduce heat to medium. Add diced onion, carrots, and celery to the pot and sauté until softened, about 5 minutes. Stir in minced garlic and tomato paste; cook for 1 minute more.
04 - Pour in red wine, scraping up browned bits from the bottom. Simmer for 2–3 minutes. Add beef broth, thyme, rosemary, and bay leaves.
05 - Return short ribs to the pot, ensuring they are mostly submerged. Bring to a simmer, cover, and transfer to the oven. Braise for 2.5 to 3 hours until meat is tender and falling off the bone.
06 - Remove pot from oven. Discard herbs and bay leaves. Skim excess fat and shred meat from bones if desired, returning it to the sauce.
07 - Thirty minutes before short ribs are done, bring water to a boil in a medium saucepan. Whisk in polenta gradually. Reduce heat to low and cook, stirring frequently, until thick and creamy, approximately 25–30 minutes.
08 - Stir in whole milk, unsalted butter, and grated Parmesan. Season with salt and pepper to taste.
09 - Spoon creamy polenta onto plates and top generously with braised short ribs and sauce.