Set the beef roast out for an hour before you start the recipe, to bring to room temperature. Next, blot the roast dry with a paper towel, on all sides. Generously season with an even coating of kosher salt and fresh ground black pepper, on all sides.
Preheat oven to 300° F. Place butter and olive oil in a 6-quart Dutch oven, over medium-high heat until hot. Sear the meat for 4 to 5 minutes on both sides, do not move the meat around the pot while it is searing. Reduce heat and remove meat from the pan and set aside.
Using the juices from the meat, saute the mirepoix over medium heat, starting with the carrots. Add additional butter or olive oil if necessary and cook the carrots until they are golden-caramel in color. Add the celery and onion and saute and stir for another 4 or 5 minutes until tender. Add the anchovies and stir for a couple more minutes until they are melted into the mirepoix.
Add the wine and stock to the pot to deglaze and be sure to stir up the brown bits until they are released and dissolved in the liquid. Stir in thyme leaves and return the meat to the pot.
Cover the Dutch oven and place in oven. Allow it to braise for 3 to 4 hours. Add (optional) additional vegetables about 45 minutes before removing from oven. The braised beef is ready to come out of the oven when you can shred it with a fork.
After you remove the braised beef from the oven, allow the meat to rest in the braising liquid until ready to serve. Remove meat from the Dutch oven and reduce braising liquid, if desired, then serve with the braised beef.
For additional vegetables, consider 8 oz. portabella mushrooms and more carrots.Other than anchovies, some additives to the mirepoix could include citrus zest, fresh ginger, or lemon grass.Garnish with additional fresh thyme, when serving the braised beef, if desired.