01 - Set the oven temperature to 325°F.
02 - Pat the short ribs dry and season generously with salt and black pepper.
03 - Heat olive oil in a large Dutch oven over medium-high heat and brown the ribs on all sides for about 8 minutes. Remove and set aside.
04 - Add onion, carrots, and celery to the pot and cook until softened, about 5 minutes. Add garlic and sauté for 1 more minute.
05 - Stir in tomato paste and cook for 2 minutes to deepen flavor.
06 - Pour in red wine, scraping up browned bits from the bottom, then simmer for 5 minutes to reduce slightly.
07 - Add beef stock, rosemary, thyme, bay leaves, and return short ribs to the pot. Bring to a simmer.
08 - Cover and transfer to the oven, braising for 2 to 2 1/2 hours until meat is fork-tender.
09 - While ribs cook, bring water or broth to a boil. Gradually whisk in cornmeal, then reduce heat to low and cook, stirring frequently, until thick and creamy, about 30 to 40 minutes.
10 - Stir in butter and Parmesan cheese, seasoning with salt and pepper to taste.
11 - Remove ribs from braising liquid, skim off excess fat, discard herb stems and bay leaves, and simmer the sauce on stovetop to reduce slightly if desired.
12 - Plate the short ribs atop creamy polenta and spoon sauce over the top.