01 - Preheat oven to 325°F. Season short ribs generously with salt and black pepper.
02 - Heat olive oil in a large heavy ovenproof pot over medium-high heat and sear the ribs on all sides until browned, about 8 to 10 minutes. Remove ribs and set aside.
03 - Add diced onion, carrots, and celery to the same pot and cook until softened, about 5 to 7 minutes. Add minced garlic and cook for an additional minute.
04 - Stir in tomato paste and cook for 2 minutes. Pour in red wine, scraping the bottom of the pot to deglaze, and simmer until slightly reduced, approximately 5 minutes.
05 - Add beef broth, rosemary, thyme, and bay leaves. Return short ribs along with their juices to the pot and bring to a simmer.
06 - Cover the pot and transfer to the oven. Braise until meat is tender and falling off the bone, 2 ½ to 3 hours.
07 - About 30 minutes before ribs are done, bring water to a boil in a medium saucepan. Gradually whisk in polenta.
08 - Reduce heat to low and cook polenta, stirring frequently, until thickened and creamy, approximately 20 to 25 minutes.
09 - Stir in whole milk, unsalted butter, and grated Parmesan. Season with salt and pepper to taste. Keep warm over very low heat, adding more milk if needed to achieve desired creaminess.
10 - Remove short ribs from braising liquid. Discard herb sprigs and bay leaves. Skim excess fat from the sauce and simmer to thicken if desired.
11 - Ladle creamy polenta into serving bowls, top with braised short ribs, and spoon sauce generously over the dish.