01 - Set the oven temperature to 325°F.
02 - Pat short ribs dry with paper towels and season generously with salt and black pepper.
03 - Heat olive oil in a heavy pot over medium-high heat and sear ribs on all sides until deeply browned, approximately 3 to 4 minutes per side. Remove and set aside.
04 - Reduce heat to medium, add diced onion, carrots, and celery; sauté for about 5 minutes until softened. Stir in minced garlic and tomato paste and cook for 1 minute.
05 - Pour in red wine, scraping browned bits from the pot. Allow to simmer for 2 to 3 minutes.
06 - Add beef broth, thyme sprigs, rosemary sprigs, and bay leaves to the pot.
07 - Return short ribs to the pot, submerging mostly in liquid. Bring to a simmer, cover, and transfer to the oven.
08 - Braise for 2.5 to 3 hours, until meat is fork-tender and falling off the bone.
09 - Remove pot from oven, discard herb sprigs and bay leaves, skim excess fat, shred meat off bones if desired, and return meat to sauce.
10 - Approximately 30 minutes before ribs are done, bring water to a boil in a saucepan. Slowly whisk in polenta, reduce heat to low, and cook while stirring frequently until thick and creamy, about 25 to 30 minutes.
11 - Stir in whole milk, unsalted butter, and grated Parmesan cheese. Season with salt and pepper to taste.
12 - Spoon creamy polenta into bowls and top generously with braised short ribs and sauce.