Preheat oven to 325 degrees. Season the chuck roast generously on all sides with salt and pepper.
Heat oil in a large Dutch oven over medium-high heat. Place roast in Dutch oven and brown on all sides, 2 to 3 minutes per side. Place roast on a plate and set aside.
Add onion, 2 of the carrots, and the fresh herbs to the Dutch oven. Cook until the vegetables are light brown and the onions soft, stirring frequently, about 3 to 4 minutes.
Place the roast back in the Dutch oven. Add the wine and enough broth to nearly cover the roast and bring to a boil. Put a lid on the Dutch oven and place in the oven for 2 hours and 30 minutes.
Add potatoes and remaining carrots to Dutch oven and place back in oven for an additional 40 to 60 minutes. When the meat shreds easily with a fork and the potatoes are tender, it is done cooking.
Place roast on a large serving platter. Remove the herb stems from the Dutch oven and skim the fat off of the top of the juices. Pour the juice and vegetables over the roast and serve.