01 - Preheat oven to 325°F (160°C).
02 - Generously season beef cheeks with salt and freshly ground black pepper.
03 - Heat olive oil in a large heavy ovenproof pot over medium-high heat. Brown beef cheeks on all sides in batches if needed. Remove and set aside.
04 - In the same pot, add chopped onion, diced carrots, and celery. Cook for 6 to 8 minutes, stirring occasionally until softened. Add minced garlic and cook an additional minute.
05 - Stir in tomato paste and cook for 2 minutes until it darkens.
06 - Pour in dry red wine, scraping up any browned bits from the pot. Bring to a simmer and cook for 5 minutes to reduce slightly.
07 - Add beef stock, fresh thyme, rosemary, and bay leaves. Return beef cheeks to the pot, ensuring they are mostly submerged.
08 - Bring contents to a simmer, cover pot, and transfer to the oven. Braise for 2.5 to 3 hours until the meat is tender and easily pierced with a fork.
09 - Toward the end of braising, bring water to a boil in a saucepan. Gradually whisk in coarse cornmeal. Reduce heat to low and cook, stirring frequently, for 25 to 30 minutes until thick and creamy.
10 - Stir in unsalted butter and grated Parmesan cheese. Season with salt to taste and keep warm.
11 - Remove beef cheeks from the pot, discarding herbs and bay leaves. Optionally, simmer the remaining liquid on the stove to reduce into a sauce.
12 - Plate the beef cheeks on a bed of creamy polenta, spoon over the reduced sauce as desired.