Season the beef cheeks generously with salt and freshly ground black pepper. Heat the olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Sear the cheeks on all sides until deeply golden brown. Remove and set aside.
In the same pot, add the diced onion, carrot, celery, and minced garlic. Cook, stirring occasionally, until the vegetables are softened and fragrant, about 5-7 minutes.
Stir in the tomato paste and cook for 2-3 minutes, allowing it to caramelize slightly and deepen its flavor.
Deglaze the pot with the red wine, scraping up any browned bits from the bottom. Simmer for 5 minutes, or until the wine has reduced slightly.
Return the beef cheeks to the pot. Add the crushed tomatoes, beef stock, bay leaves, and fresh rosemary. Bring to a gentle simmer.
Cover the pot tightly with a lid and cook on low heat for 3-4 hours, or until the beef cheeks are incredibly tender and easily shredded with a fork.
Remove the beef cheeks from the pot and shred them with two forks. Return the shredded meat to the sauce, discarding the bay leaves and rosemary sprig, and stir to combine.
Serve the ragu immediately over freshly cooked pasta (such as pappardelle or tagliatelle) or creamy polenta. Garnish generously with grated Parmesan cheese and a sprig of fresh rosemary.
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