When the roast's internal temperature reaches 155°F, begin making the stew.
Start by placing a large Dutch oven on the stovetop over medium heat. Add olive oil, carrots, onions, and celery. Sauté for 10 minutes or until they are soft and translucent but not browned. Add garlic and cook another 1 minute while stirring.
Add the white wine or your preferred wine choice and bring to a simmer for 5 minutes. Add the tomatoes that are crushed in the can, or you can crush them yourself as you add them to the pot, stock, rosemary, thyme, chili pepper flakes, salt, and pepper bring back to a simmer.
At this point, the roast will be at or close to 165°F. When this happens, place the roast into the braising liquid and cover. Place the pot with the chuck roast in it onto the smoker.