01 - Preheat oven to 300°F. Position the rack in the lower third of the oven for even heat distribution.
02 - Pat the beef chuck roast thoroughly dry with paper towels. Season generously on all sides with kosher salt and freshly ground black pepper.
03 - Heat olive oil in a large Dutch oven over medium-high heat until shimmering. Sear the roast on all sides until a deep golden-brown crust forms, approximately 4–5 minutes per side. Transfer the seared roast to a plate and set aside.
04 - Add the quartered onion, carrot pieces, and celery chunks to the same pot. Cook for 4–5 minutes until the vegetables are lightly caramelized. Stir in the smashed garlic and tomato paste, cooking for 1 minute until fragrant.
05 - Pour in the dry red wine, scraping the bottom of the pot with a wooden spoon to release all browned bits. Let the liquid simmer for 2–3 minutes to reduce slightly and concentrate the flavors.
06 - Return the seared roast to the pot. Add the beef broth, dried thyme, fresh rosemary sprigs, and bay leaves. Bring the liquid to a gentle simmer, then cover tightly with the lid.
07 - Transfer the covered Dutch oven to the preheated oven. Braise for 3 hours, or until the roast is fork-tender and the vegetables are soft and deeply flavored.
08 - Remove from the oven and discard the bay leaves and rosemary stems. Slice or shred the beef and serve alongside the braised vegetables, spooning the rich pan juices over the top.