Preheat oven to 300°F.
Remove the chuck roast from its packaging, leaving any twine around the roast intact.
Combine the flour, salt, and pepper on a sheet of parchment paper or large plate. Dip each side of the roast into the flour mixture to coat all sides.
Heat the oil in a large stockpot or Dutch oven over medium heat.
Add the flour-coated roast to the Dutch oven and brown well on each side.
Remove the roast from the pot and add the carrots and onions. Add a bit more oil if needed.
Cook the vegetables over medium heat until onions just begin to brown. Remove from heat.
Add the beef broth and the browned roast into the pan over the vegetables. Cover with a lid and place in the oven to cook for about 3 hours. The roast is done when it easily falls apart if you pull at it with a fork.
Calories: 384kcal | Carbohydrates: 14g | Protein: 32g | Fat: 22g | Saturated Fat: 8g | Cholesterol: 104mg | Sodium: 840mg | Potassium: 729mg | Fiber: 2g | Sugar: 3g | Vitamin A: 7663IU | Vitamin C: 4mg | Calcium: 50mg | Iron: 4mg