Season chuck roast all over with salt and pepper. Pour 1 tablespoon oil in a large, Dutch oven over medium-high heat.
Add beef to Dutch oven and sear on each side for 5 minutes. Remove from pot and set aside.
Add remaining oil to Dutch oven followed by onions, carrots and celery and saute for 4-5 minutes. Add the garlic and saute for another 2 minutes. Season with salt and pepper.
Stir oregano, tomato paste and balsamic vinegar to mixture and stir together.
Deglaze pot with broth, scraping up any brown bits from the bottom of the pot.
Stir in crushed tomatoes, diced tomatoes and basil leaves and stir together.
Add beef back into pot and reduce heat to medium-low to low. Cover and (barely) simmer for 3 to 3 ½ hours or until beef is for tender and falling apart.
Shred beef with 2 forks and stir into sauce until evenly combined. Season with salt and pepper to taste.
Pour water into a saucepan and place over medium-high heat. Season with salt and pepper. Bring water to a boil and whisk in the polenta in a slow and steady stream until fully combined.
Lower heat to medium and simmer for 30 to 40 minutes, while constantly stirring, or until the mixture thickens (to a porridge consistency). Remove polenta from heat and stir in the butter and shredded gruyere a little at a time, until mixture is creamy and smooth. Season with salt and pepper to taste.
Pour polenta into bowls and top with beef ragu. Top each bowl with more grated Parmesan and fresh basil leaves (optional). Serve.
