About 30 minutes – 1 hour before you’d like to begin cooking, pull the beef chuck roast from the refrigerator & allow it to come up to room temperature. Just before cooking, use a paper towel to pat all sides of the roast as dry as possible. Season liberally with kosher salt and ground black pepper – a good rule of thumb is 1 teaspoon kosher salt per pound of meat.
Add the olive oil to a large, heavy-bottomed pot or Dutch oven (at least 5-qt capacity) over medium-high heat. Once the oil is hot & simmering, carefully add the chuck roast. Cook 4-5 minutes per side, until deeply browned. Don’t forget to brown the skinnier edges! Once seared, transfer to a plate & set aside.
Add the carrots, celery, onion, and garlic to the pot used to sear the chuck roast. Season with ½ teaspoon kosher salt and ground black pepper as desired. Stir to combine. Cook 2-3 minutes, just until fragrant.
Pour in the red wine, using a wooden spoon to scrape the bottom of the pot. Cook 1-2 minutes, then add the seared beef chuck roast back into the skillet, nestling it into the vegetables. Add in the beef stock, tomato paste, Worcestershire sauce, Dijon mustard, bay leaves, fresh rosemary and thyme. Stir to combine well. Bring the pot up to a boil, then reduce heat to maintain a very gentle simmer. Cover and braise, stirring occasionally, for 3 – 3 ½ hours, or until the beef is tender – it’s ready once it shreds easily with the twist of a fork.
Once the red wine braised beef is tender, carefully transfer the roast to a plate or cutting board. At this point, you can remove & discard the spent herbs and bay leaves from the pot, as well. If desired, thicken the braising liquid. Skim any excess fat from the top of the braising liquid, then return to medium heat. Once bubbling, stir in the flour slurry. Simmer, stirring occasionally, for 3-4 minutes until thickened as desired. Taste and season with additional kosher salt & ground black pepper as needed.