Step 1: Preheat oven to 325°F (160°C). Pat the chuck roast dry with paper towels. Season generously on all sides with salt and freshly ground black pepper.
Step 2: Heat 2 tablespoons of olive oil in a large Dutch oven or oven-safe pot over medium-high heat. Once hot, sear the roast on all sides until deeply browned, about 3-5 minutes per side. Remove the roast and set aside.
Step 3: Add the chopped onion to the same pot, adding a little more oil if needed. Sauté over medium heat for 5-7 minutes until softened and lightly caramelized, scraping up any browned bits from the bottom of the pot.
Step 4: Add the minced garlic and cook for another minute until fragrant. Pour in the red wine (if using), scraping the bottom of the pot with a wooden spoon to deglaze. Let the wine simmer for 2-3 minutes to reduce slightly.
Step 5: Stir in the beef broth, tomato paste, Worcestershire sauce, fresh rosemary, and fresh thyme. Bring the mixture to a gentle simmer.
Step 6: Return the seared chuck roast to the pot. It should be mostly submerged in the liquid. If not, add a little more beef broth.
Step 7: Cover the Dutch oven tightly and transfer it to the preheated oven. Braise for 2.5 to 3 hours, or until the meat is fork-tender.
Step 8: Remove the pot from the oven. Carefully transfer the roast to a cutting board and tent loosely with foil. Allow it to rest for at least 15-20 minutes.
Step 9: While the meat rests, add the carrots and potatoes to the simmering liquid in the Dutch oven. Cook on the stovetop or return to the oven (uncovered) for 20-30 minutes, or until the vegetables are tender.
Step 10: Taste the sauce and adjust seasoning as needed. If you prefer a thicker sauce, you can remove some liquid, whisk in a cornstarch slurry (1 tbsp cornstarch mixed with 2 tbsp cold water), and simmer until thickened.
Step 11: Shred the tender beef with two forks, or slice against the grain. Serve hot with the braising liquid, carrots, and potatoes, garnished with fresh parsley if desired.