01 - Set oven temperature to 325°F (165°C).
02 - Pat beef short ribs dry and season generously with kosher salt and freshly ground black pepper.
03 - Heat olive oil in a large Dutch oven over medium-high heat. Brown ribs on all sides in batches if necessary. Transfer ribs to a plate.
04 - Add diced onion, carrots, and celery to the pot; cook until softened, about 5 minutes. Stir in minced garlic and cook for 1 additional minute.
05 - Incorporate tomato paste into vegetables and cook, stirring, for 2 minutes.
06 - Pour in dry red wine, scraping the bottom to release browned bits. Simmer for 5 minutes to slightly reduce.
07 - Add beef broth, crushed tomatoes, thyme, rosemary, and bay leaves. Return short ribs and accumulated juices to the pot and bring to a simmer.
08 - Cover the pot and transfer to the oven. Cook for 2.5 to 3 hours until ribs are fork-tender and meat easily separates from the bone.
09 - About 30 minutes before ribs finish, bring water to a boil in a saucepan. Gradually whisk in polenta, reduce heat to low, and cook stirring frequently for 20–25 minutes until thick and creamy.
10 - Stir in whole milk, unsalted butter, and grated Parmesan cheese into the polenta. Season with salt and pepper to taste and keep warm.
11 - Remove ribs from oven, discard herb sprigs and bay leaves, and skim excess fat from the sauce. Adjust seasoning if necessary. Serve ribs and sauce over creamy polenta, garnished with extra Parmesan or fresh herbs if desired.