01 - Preheat oven to 325°F (165°C).
02 - Pat short ribs dry with paper towels and season generously with salt and pepper on all sides.
03 - In a large Dutch oven, heat olive oil over medium-high heat. Sear short ribs on all sides until deeply browned, about 3-4 minutes per side. Remove from pot and set aside.
04 - Add onion, carrots, and celery to the same pot. Sauté for 5-7 minutes until softened. Add garlic and tomato paste; cook for 2 minutes, stirring constantly.
05 - Pour in red wine, scraping up browned bits from the bottom of the pot. Simmer for 5 minutes to reduce slightly.
06 - Add beef stock, thyme sprigs, rosemary sprigs, and bay leaves. Return short ribs to the pot, ensuring liquid nearly covers the meat.
07 - Bring to a simmer, cover tightly, and transfer to the oven. Braise for 2 to 2½ hours until ribs are very tender and falling off the bone.
08 - When ribs are almost done, bring 4 cups water and salt to a boil in a saucepan. Slowly whisk in polenta, stirring constantly to prevent lumps.
09 - Reduce heat to low and cook polenta, stirring often, for 25-30 minutes until thick and creamy.
10 - Stir in butter, Parmesan cheese, and milk. Adjust seasoning with additional salt if needed.
11 - Remove short ribs from oven. Discard herb sprigs and bay leaves. Skim excess fat from the sauce surface if desired. Serve short ribs over creamy polenta, spooning sauce generously over the top.