Preheat and prep: Preheat oven to 300°F. Pat the chuck roast completely dry with paper towels and season all over with salt and black pepper.
Sear the roast: Heat olive oil in a Dutch oven over medium-high heat until shimmering. Brown the roast for 4-5 minutes on each broad side without moving it until a deep crust forms. Briefly brown the edges as well. Transfer to a plate and set aside.
Cook the onion: Lower the heat to medium. Add the sliced onion to the same pot and cook stirring occasionally for 12-15 minutes until softened and genuinely golden. Add chopped garlic and cook for 1 minute until fragrant. Add tomato paste and cook stirring constantly for 2 minutes until it darkens slightly.
Deglaze: Pour in the red wine and scrape up all the browned bits from the bottom of the pot. Simmer for 3-5 minutes until reduced by roughly half.
Start the braise: Return the roast and any accumulated juices to the pot. Add thyme, rosemary, bay leaf, and Worcestershire sauce. Pour in enough beef broth to reach about halfway up the roast. Bring to a gentle simmer, cover tightly, and transfer to the oven for 2 hours.
Add the vegetables: After 2 hours nestle the potatoes, carrots, and celery around the roast mostly submerged in the liquid. Cover and cook for another 1 to 1½ hours, checking after 1 hour. The roast is done when a fork slides in easily and the meat pulls apart with little resistance. If the vegetables become tender before the meat remove them and return them to warm through at the end. If needed continue in 30-minute increments.
Finish the braising liquid: Transfer the beef and vegetables to a platter and loosely cover. Remove and discard the herb stems and bay leaf. Skim any excess fat from the surface of the liquid. Stir in 1 tsp red wine vinegar, taste, and add the second teaspoon if you want more brightness. Adjust salt and pepper. At this point you can spoon the braising liquid straight over the roast — it's deeply flavored and completely delicious as-is.
Optional gravy: If you want a thicker sauce bring the braising liquid to a simmer. Mash the softened butter and flour together into a smooth paste. Whisk the paste into the simmering liquid a little at a time and simmer for 5-8 minutes until lightly thickened. Taste and adjust seasoning.
Serve: Spoon the braising liquid or gravy over the roast and vegetables and finish with fresh parsley if using. Enjoy on its own or eat it with my garlic mashed potato recipe!