01 - Preheat oven to 325°F. Pat ribs dry and season generously with salt and pepper.
02 - Heat olive oil in a large Dutch oven over medium-high heat. Brown ribs on all sides in batches if necessary, then remove to a plate.
03 - Add diced onion, carrots, and celery to the pot and cook until softened, about 5 minutes. Add garlic and cook for 1 additional minute.
04 - Stir in tomato paste and cook for 2 minutes. Pour in red wine, scraping browned bits from the pot and simmer until slightly reduced, about 5 minutes.
05 - Pour in beef broth and crushed tomatoes. Add thyme, rosemary, and bay leaves. Return ribs along with juices to the pot and bring to a simmer.
06 - Cover the pot and transfer to the oven. Braise for 2.5 to 3 hours until ribs are tender and meat falls off the bone.
07 - About 30 minutes before ribs finish, bring water to a boil in a saucepan. Slowly whisk in polenta, reduce heat to low, and cook, stirring frequently, for 20-25 minutes until thickened and creamy.
08 - Stir in whole milk, butter, and grated Parmesan. Season with salt and pepper. Keep warm until serving.
09 - Remove ribs from oven. Discard herb sprigs and bay leaves. Skim excess fat from the sauce and adjust seasoning if needed.
10 - Serve short ribs and sauce atop creamy polenta. Garnish with extra Parmesan and fresh herbs if desired.