01 - Preheat oven to 325°F. 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, then transfer to a plate.
02 - Reduce heat to medium. Add onion, carrots, and celery to the pot. Cook for 6 to 8 minutes, stirring occasionally, until softened. Add garlic and tomato paste; cook for 1 minute until fragrant.
03 - Pour in red wine, scraping the bottom to release browned bits. Let simmer for 2 to 3 minutes to reduce slightly.
04 - Add crushed tomatoes, thyme sprigs, bay leaf, and beef stock to the pot. Return browned beef along with any accumulated juices. 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.
05 - Remove thyme sprigs and bay leaf. Shred beef with two forks, mixing it back into the sauce. Maintain on low heat to keep warm.
06 - 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.
07 - Stir in whole milk, unsalted butter, and grated Parmigiano-Reggiano cheese. Season with salt to taste.
08 - Spoon creamy polenta into bowls. Top generously with braised beef ragu. Garnish with additional grated cheese and chopped fresh parsley if desired.