01 - Preheat the oven to 325°F (160°C).
02 - Season beef cheeks generously 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, then remove and set aside.
04 - Add chopped onion, diced carrots, and celery to the pot. Cook, stirring occasionally, for 6 to 8 minutes until softened. Stir in minced garlic and cook for 1 additional minute.
05 - Incorporate tomato paste, cooking and stirring for 2 minutes until it darkens slightly.
06 - Pour in dry red wine while scraping browned bits from the pot. Bring to a simmer and reduce for 5 minutes.
07 - Add beef stock, fresh thyme, rosemary, and bay leaves to the pot. Return beef cheeks ensuring they are mostly submerged.
08 - Bring mixture to a simmer, cover, and transfer to the preheated oven. Braise for 2.5 to 3 hours until beef cheeks are fork-tender.
09 - Near the end of braising, bring water to a boil in a saucepan. Gradually whisk in polenta, reduce heat to low, and cook while stirring frequently for 25 to 30 minutes until thick and creamy.
10 - Stir butter and grated Parmesan cheese into the polenta. Season with salt to taste.
11 - Remove beef cheeks from the braising liquid. Discard herbs and bay leaves. Simmer the remaining liquid on stovetop to reduce to a sauce consistency if desired.
12 - Place braised beef cheeks over creamy polenta and spoon sauce atop before serving.