Preheat the oven to 325°F (163°C). Place the rack in the center of the oven.
In a small bowl, mix together the salt, garlic powder, onion powder, black pepper, and mustard powder. Pat the chuck roast dry with paper towels, then rub the spice mix evenly all over the surface of the roast. Press it in firmly to help the seasoning stick.
Heat 1 tablespoon olive oil in a large Dutch oven over medium-high heat. When the oil is shimmering but not smoking, carefully add the roast. Sear it for 3 to 4 minutes per side, or until each side develops a deep golden brown crust. This step builds flavor, so don’t rush it. Use tongs to turn the roast for even browning.
Remove the Dutch oven from the heat. Arrange the sliced onion, carrots, potatoes, mushrooms, and crushed garlic cloves around the roast in the pan. Spread them evenly to ensure they roast properly.
In a medium bowl, whisk together the beef broth, balsamic vinegar, brown sugar, Worcestershire sauce, Dijon mustard, and cornstarch until smooth and well combined. Pour the mixture evenly over the roast and vegetables, making sure the meat is partially submerged.
Nestle the rosemary and thyme sprigs and bay leaves into the pot. These will infuse the entire dish with aromatic flavor as it cooks.
Place the lid on the Dutch oven and transfer it to the preheated oven. Roast at 325°F for 1 hour. Then, reduce the temperature to 300°F (149°C) and continue cooking for another 1½ to 2 hours. The roast is done when it easily shreds apart with tongs or a fork. If it resists, continue cooking in 20-minute increments, checking each time.
Remove the pot from the oven and let it rest, covered, for 15 minutes to allow the juices to settle. Remove and discard the herb sprigs and bay leaves. Transfer the roast to a cutting board or serving platter and shred it into chunks or strands. Serve with the vegetables, and spoon the flavorful sauce over the top.