Preheat your oven to 350°F (175°C). Using paper towels, pat the chuck roast pieces very dry to help them brown better. Generously season the beef all over with kosher salt and freshly ground black pepper.
Heat neutral-flavored oil in a large braiser or Dutch oven over medium-high heat until shimmering. Add the seasoned beef chunks and sear them on all sides until a deep golden brown crust forms, about 3 to 4 minutes per side. Work in batches if needed to avoid crowding the pan. Transfer the browned beef to a plate and set aside.
Reduce the heat to medium-low. Add the chopped onion, sliced leeks, and thinly sliced garlic to the same pan. Sauté, stirring occasionally, until the onions and leeks are just tender, which should take about 5 minutes. The browned bits on the bottom of the pan will add wonderful flavor.
Pour in the dry red wine and beef broth, scraping the bottom to deglaze any flavorful bits. Season the liquid lightly with salt and pepper. Bring the mixture up to a simmer. Return the browned beef (from Step 2) to the pot, then nestle the carrots, thyme sprigs, and bay leaves around the meat. The beef should sit just above the liquid level for the perfect braise. Cover the pan and transfer it to the preheated oven.
Bake the covered braise in the preheated oven for 2 1/2 hours. Then, remove the lid and continue cooking for an additional 30 to 45 minutes, until the beef is extremely tender and can be easily shredded with a fork. I occasionally check at this point and add a splash of broth if it looks too dry.
Remove the braiser or Dutch oven from the oven. Skim off and discard the layer of fat on top of the braising liquid. Cover the meat and let it rest in the juices for at least 45 minutes; this helps the flavors meld and the meat keep moist. When ready to serve, gently rewarm the beef on the stove if needed. Serve over mashed potatoes and, for a fresh finish, garnish with minced chives if desired.