01 - Preheat the oven to 325°F (165°C).
02 - Pat the beef short ribs dry and season liberally with kosher salt and black pepper.
03 - Heat olive oil in a large Dutch oven over medium-high heat. Brown the short ribs on all sides in batches, then transfer to a plate.
04 - Add diced onion, carrots, and celery to the pot. Sauté for about 5 minutes until softened. Add minced garlic and cook for 1 more minute.
05 - Stir in the tomato paste and cook for 2 minutes to develop flavor.
06 - Pour in the red wine, scraping up browned bits from the bottom. Simmer for 5 minutes to reduce slightly.
07 - Add beef broth, crushed tomatoes, thyme, rosemary, and bay leaves. Return the short ribs and any accumulated juices to the pot and bring to a simmer.
08 - Cover the pot and transfer to the oven. Braise for 2.5 to 3 hours until the meat is tender and falling off the bone.
09 - About 30 minutes before the 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 creamy.
10 - Stir in whole milk, unsalted butter, and grated Parmesan cheese. Season with salt and pepper and keep warm.
11 - Remove the ribs from the oven. Discard herb sprigs and bay leaves. Skim excess fat from the sauce. Adjust seasoning if necessary.
12 - Ladle the short ribs and sauce over the creamy polenta. Garnish with additional Parmesan and fresh herbs as desired.