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