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. Brown in batches until golden on all sides. Transfer to a plate.
03 - Reduce heat to medium. Add onion, carrots, and celery to the pot. Cook, stirring occasionally, for 6 to 8 minutes until softened. Add garlic and tomato paste, cooking for 1 minute until fragrant.
04 - Pour in red wine, scraping up browned bits from the bottom. Let simmer for 2 to 3 minutes.
05 - Add crushed tomatoes, thyme sprigs, bay leaf, and beef stock. Return browned beef and juices to the pot and stir to combine.
06 - Bring mixture to a simmer, cover, and transfer to the oven. Braise for 2 to 2.5 hours until beef is fork-tender.
07 - Remove thyme and bay leaf. Shred beef with forks and stir into sauce. Keep warm over low heat.
08 - Bring water and a pinch of salt to a boil in a large saucepan. Gradually whisk in polenta. Reduce heat to low and cook, whisking frequently, for 25 to 30 minutes until thick and creamy.
09 - Stir in whole milk, butter, and Parmigiano-Reggiano. Season with salt to taste.
10 - Spoon creamy polenta into bowls. Top generously with braised beef ragu. Garnish with extra grated cheese and chopped parsley if desired.