01 - Pat the beef short ribs dry with paper towels and season generously on all sides with salt and freshly ground black pepper.
02 - Heat olive oil in a large Dutch oven or ovenproof pot over medium-high heat. Sear the short ribs on all sides until deeply browned, about 3-4 minutes per side. Remove from pot and set aside.
03 - In the same pot, add onion, carrots, and celery. Cook, stirring frequently, until softened, about 5 minutes. Add minced garlic and cook for 1 minute more until fragrant.
04 - Stir in tomato paste and cook for 2 minutes, stirring constantly, until the paste darkens slightly and develops a rich color.
05 - Pour in red wine, using a wooden spoon to scrape up any browned bits from the bottom of the pot. Simmer for 3-4 minutes to reduce slightly and concentrate flavors.
06 - Add beef stock, thyme sprigs, rosemary sprigs, and bay leaves. Return the seared short ribs to the pot, ensuring they are mostly submerged in the liquid.
07 - Bring to a simmer, then cover with a tight-fitting lid. Transfer to a preheated oven at 325°F and braise for 3 hours, or until the meat is fork-tender and falling off the bone.
08 - Remove the short ribs from the pot and set aside. Strain the sauce through a fine-mesh sieve if desired, and skim excess fat from the surface. Discard the herb sprigs and bay leaves.
09 - In a medium saucepan, bring the water or chicken stock to a rolling boil over high heat.
10 - Slowly whisk in the coarse cornmeal, stirring constantly to prevent lumps. Reduce heat to low and cook, stirring frequently, for 25-30 minutes until thick and creamy.
11 - Remove from heat and stir in butter and grated Parmesan cheese until melted and fully incorporated. Season with salt and freshly ground black pepper to taste.
12 - Spoon a generous bed of creamy polenta onto each serving plate. Top with braised short ribs and ladle the rich sauce over the meat and polenta. Serve immediately while hot.