Preheat the oven to 325°F (160°C). Pat the Boneless Beef Chuck Roast dry and season generously on all sides with Kosher Salt and freshly ground Black Pepper. Dredge the roast in All-Purpose Flour, shaking off any excess.
Heat a few tablespoons of Vegetable Oil in a heavy Dutch oven or ovenproof pot over medium-high heat. When the oil is shimmering, sear the roast on all sides until deeply browned, about 3–4 minutes per side. Transfer the browned roast to a plate and set aside.
Reduce the heat to medium and add the chopped Yellow Onion to the pot; cook until softened, about 5 minutes. Add minced Garlic and cook 30–60 seconds more until fragrant.
Add the chopped Carrot and Celery to the pot and cook, stirring occasionally, until they begin to soften, about 4–5 minutes.
Stir in the Tomato Paste and cook for 1–2 minutes to deepen its flavor. Pour in the Worcestershire Sauce and scrape the bottom of the pot to loosen any browned bits.
Return the roast to the pot and add enough Beef Broth to come about halfway up the sides of the roast. Nestle the halved Yukon Gold Potatoes around the meat.
Tuck sprigs of Thyme, Rosemary, and a Bay Leaf into the liquid. Bring the braising liquid to a gentle simmer on the stovetop.
Cover the pot and transfer it to the preheated oven. Braise until the meat is fork-tender, about 2½ to 3 hours, checking once or twice to ensure the liquid is not evaporating too quickly (add a splash of broth if needed).
Carefully remove the pot from the oven. Transfer the roast and potatoes to a cutting board and let the meat rest for 10–15 minutes. Remove and discard the herb stems and bay leaf from the sauce.
If desired, skim fat from the surface of the braising liquid and simmer the sauce on the stovetop to reduce and thicken slightly. Slice or shred the rested roast, season the sauce to taste with additional Kosher Salt and Black Pepper if needed, and serve the meat with the potatoes and vegetables, spooning plenty of sauce over everything.
