01 - Preheat oven to 325°F.
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 ribs and set aside on a plate.
04 - Add onion, carrots, and celery to the same pot. Sauté for 5–7 minutes until softened and beginning to brown. Add minced 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 with a wooden spoon. Simmer for 5 minutes until slightly reduced.
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 on the stovetop, then cover tightly with a lid. Transfer to the oven and braise for 2–2½ hours until meat is fork-tender and falling off the bone.
08 - When ribs are nearly finished, bring 4 cups water and salt to a boil in a saucepan. Slowly whisk in polenta in a steady stream to prevent lumps.
09 - Reduce heat to low and cook polenta, stirring frequently, for 25–30 minutes until thickened and creamy.
10 - Stir in butter, Parmesan cheese, and milk. Adjust seasoning with additional salt if needed. Keep warm over low heat until ready to serve.
11 - Remove short ribs from oven. Discard herb sprigs and bay leaves. Skim excess fat from sauce surface if desired. Serve short ribs over creamy polenta, ladling sauce generously over the top.