01 - Preheat your oven to 325°F to prepare for braising.
02 - Pat the short ribs thoroughly dry with paper towels, then season generously on all sides with kosher salt and freshly ground black pepper.
03 - Heat olive oil in a large Dutch oven over medium-high heat. Sear short ribs on all sides until deeply browned, approximately 3-4 minutes per side. Remove browned ribs and set aside on a plate.
04 - Add diced onion, carrots, and celery to the same pot. Sauté for 5-7 minutes until vegetables are softened and beginning to caramelize. Add minced garlic and tomato paste, cooking for 2 additional minutes while stirring constantly to prevent burning.
05 - Pour in the red wine, using a wooden spoon to scrape up any browned bits from the bottom of the pot. Allow the mixture to simmer for 5 minutes until slightly reduced.
06 - Add beef stock, fresh thyme, rosemary, and bay leaves to the pot. Return the seared short ribs to the Dutch oven, arranging them so the liquid nearly covers the meat.
07 - Bring the liquid to a simmer, then cover tightly with the lid. Transfer to the preheated oven and braise for 2-2½ hours until the meat is fork-tender and falling off the bone.
08 - While the ribs finish braising, bring 4 cups water and salt to a boil in a medium saucepan. Slowly whisk in the coarse cornmeal in a steady stream to prevent lumps. Reduce heat to low and cook for 25-30 minutes, stirring frequently, until thickened and creamy.
09 - Remove polenta from heat and stir in unsalted butter, grated Parmesan cheese, and whole milk or heavy cream until melted and thoroughly combined. Adjust seasoning with additional salt if needed.
10 - Remove the braised short ribs from the oven. Discard the herb sprigs and bay leaves. Skim excess fat from the sauce surface if desired. Serve the short ribs over a bed of creamy polenta, spooning the reduced braising sauce generously over the top.