Preheat oven to 300F and allow chuck roast to come to room temperature. Peel and chop carrots into sticks. Clean and cut each baby potato in half or quarters if larger.
Season chuck roast on all sides generously with salt and pepper. Heat a dutch oven over medium heat. (if you don't have a dutch oven use a skillet for this step and then transfer to a roasting pan) When the pot is warm, sear the chuck roast on all sides until there is a golden brown crust - about 4 mins each side.
Remove the chuck roast from the pan and reduce the heat to medium low. Pour the tomato paste into the warm pan and let it toast for a minute. Pour in the red wine and let it bubble up and mix in with the tomato past. Pour in the beef broth and mix in while also scraping any brown bits from the bottom. Let this mixture simmer for 5 minutes.
Arrange half of the carrots and potatoes in a layer in on the edges of bottom of the dutch oven or roasting pan. Place the roast into the pot and arrange the rest of the carrots and potatoes around it. If you are using a roasting pan, pour the juice from skillet over the top. Sprinkle the whole thing with the thyme and rosemary.
Cover the dutch oven or roasting pan with a lid and place in the oven to cook. Cook for 3 hours covered at 300F. Check the meat at 3 hours - it should be fork tender and very easy to cut or even tear apart. IF you used a piece of meat that is large than 3lbs add an extra 30 minutes of cook time until it becomes super tender.
Serve the meat warm with the potatoes and carrots. Drizzle the excess juice from the pan over top.
Notes
Get a nice crust on the roast while searing - allow the chuck roast to come to room temperature. Then, season very generously with a few teaspoons of salt and pepper. Allow oil to get very hot in the pan before you let your roast sear. Only flip it once it is evenly browned on one side. The browning adds tons of flavor to the final dish.
Take your time preparing the red wine jous - the red wine gravy made from a dry red wine, beef broth and tomato paste is the thing that infuses a ton of flavor into the beef. Take your time preparing this and scraping any browned bits from the pan you used to sear the meat.
Allow the roast to rest before slicing - it is critical to let the chuck roast rest for at least 10 minutes after taking it out of the oven to make sure the juices lock in and keep the final dish moist.
If you don't have red wine or don't want to use alcohol you can use 2 tbsp of red wine vinegar and add some extra beef broth to the gravy.