Preheat an oven to 350°F. While the oven is preheating, cut the chuck into 4-5 even pieces.
Pat the beef very dry using a paper towel and generously season all sides with salt and pepper.
In a large Braiser or dutch oven, heat oil until over medium-high and simmering.
Brown meat on all sides until deeply golden brown, 3-4 minutes per side. Transfer to a plate.
Reduce heat to medium-low, add in the diced onions, carrots and celery (mirepoix) and butter and sauce until the onions are just tender, about 5 minutes.
Add tomato paste, Dijon mustard, and garlic cloves, peeled and thinly sliced and sauté for one minute.
Add the wine and stock and bring to a simmer. Season lightly with salt and pepper.
Return the meat to the pan and nestle in the thyme sprigs, and bay leaves. The meat should sit just above the liquid line. For a good braise, you don’ want it fully immersed in the liquid. Cover and transfer to the oven for 2 hours.
I like to sauté the carrots and potatoes in a pan to add some nice color before adding them back into the pot, but this is optional.
Remove lid, add in carrots and potatoes and cook for another 30-45 minutes, until the beef is fork-tender.
Remove from the oven and skim off the layer of fat on top and discard. Cover and rest the beef in the juices for at least 45 minutes. Gently re-warm on the stove before serving.