Pat the short ribs dry and season them generously with salt and pepper on all sides.

Heat the olive oil in a Dutch oven over medium-high heat. Brown the short ribs in batches until deeply colored on all sides, then remove them to a plate.

Lower the heat to medium and add the onion, carrots, and celery to the pot. Cook until the vegetables soften, about 8 minutes. Stir in the garlic and tomato paste and cook for 1 minute more.

Pour in the red wine and scrape up any browned bits from the bottom. Let the wine reduce by half, then add the beef broth, thyme, and rosemary. Return the short ribs to the pot.

Bring the liquid to a simmer, cover the pot, and transfer it to a 325°F oven. Cook for 2 1/2 to 3 hours until the meat is very tender and pulls easily from the bone.

While the ribs finish, bring the water to a boil in a saucepan. Whisk in the polenta and a pinch of salt. Reduce to low heat and stir often for 20 to 25 minutes until thick and creamy. Stir in the butter and Parmesan.

Remove the short ribs from the oven. Skim excess fat from the surface of the sauce if needed. Serve the ribs and sauce over bowls of the hot polenta and sprinkle with parsley.