01 - Preheat the oven to 325°F.
02 - Heat olive oil in a large Dutch oven over medium-high heat. Season beef with salt and pepper, then brown in batches until golden on all sides. Transfer browned beef to a plate.
03 - Reduce heat to medium and add onion, carrots, and celery to the pot. Cook for 6 to 8 minutes, stirring occasionally, until softened. Add garlic and tomato paste and cook for 1 minute until fragrant.
04 - Pour in dry red wine, scraping up browned bits from the bottom. Let simmer for 2 to 3 minutes to reduce slightly.
05 - Add crushed tomatoes, thyme sprigs, bay leaf, beef stock, and the browned beef with juices back into the pot. Stir to combine, bring to a simmer, cover, and transfer to the oven. Braise for 2 to 2.5 hours until beef is fork-tender.
06 - Remove thyme sprigs and bay leaf. Shred the beef with two forks, mixing it thoroughly into the sauce. Keep warm on low heat.
07 - Bring water and a pinch of salt to a boil in a large saucepan. Gradually whisk in polenta, reduce heat to low, and cook while whisking frequently for 25 to 30 minutes until thick and creamy.
08 - Stir milk, unsalted butter, and grated Parmigiano-Reggiano into the polenta. Season with salt to taste.
09 - Spoon creamy polenta into serving bowls. Top generously with braised beef ragu. Garnish with additional grated cheese and chopped fresh parsley if desired.