01 - Preheat the oven to 325°F.
02 - Pat short ribs dry and season generously with salt and pepper.
03 - Heat olive oil in a large ovenproof pot over medium-high heat. Sear short ribs on all sides until deeply browned, about 3 to 4 minutes per side. Remove and set aside.
04 - Reduce heat to medium. Add diced onion, carrots, and celery; cook until softened, approximately 5 minutes. Stir in garlic and tomato paste; cook for an additional minute.
05 - Pour in red wine, scraping up browned bits from the pot. Simmer for 2 to 3 minutes, then add beef broth, thyme, rosemary, and bay leaves.
06 - Return short ribs to the pot, ensuring they are mostly submerged. Bring to a simmer, cover, and transfer to the oven.
07 - Cook in the oven for 2.5 to 3 hours until meat is tender and falling off the bone.
08 - About 30 minutes before short 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, approximately 25 to 30 minutes.
09 - Stir in milk, butter, and Parmesan cheese. Season with salt and pepper to taste.
10 - Spoon polenta into bowls and top generously with braised short ribs and sauce.