01 - Set oven temperature to 325°F (165°C).
02 - Pat short ribs dry and season liberally with kosher salt and freshly ground black pepper.
03 - Heat olive oil in a large Dutch oven over medium-high heat. Brown short ribs on all sides in batches as needed, then transfer to a plate.
04 - Add diced onion, carrots, and celery to the pot and cook until softened, about 5 minutes. Stir in minced garlic and cook for an additional minute.
05 - Incorporate tomato paste and cook, stirring, for 2 minutes to deepen flavor.
06 - Pour in red wine, scraping browned bits from the bottom of the pot. Simmer for 5 minutes to reduce slightly.
07 - Stir in beef broth, crushed tomatoes, fresh thyme, rosemary, and bay leaves. Return short ribs and any accumulated juices to the pot and bring to a gentle simmer.
08 - Cover the pot and transfer to the oven. Cook for 2.5 to 3 hours, or until meat is tender and falls off 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 to 25 minutes until thick and creamy.
10 - Stir in whole milk, butter, and grated Parmesan cheese. Season with salt and pepper to taste and keep warm.
11 - Remove ribs from oven. Discard herb sprigs and bay leaves. Skim excess fat from surface and adjust seasoning if necessary.
12 - Plate short ribs with sauce atop creamy polenta. Garnish with additional Parmesan and fresh herbs if desired.