Place the oven rack low enough to fit a large Dutch oven and preheat to 325˚F (165˚C).
In a small bowl, evenly combine the flour, salt, and black pepper.
Pat the chuck roast dry with a paper towel, then rub the salted flour mixture into all sides.
Place a large Dutch oven over medium high heat and add the butter and oil.
Once thoroughly heated and the butter has melted, add the seasoned chuck roast. Sear until golden brown on all sides. Remove to a plate and set aside.
Add the onion, garlic, potatoes, and carrots to the pan and cook, stirring occasionally, until starting to brown.
Stir in the tomato paste until the vegetables are coated and continue to cook for 1-2 minutes.
Slowly pour in the red wine, scraping the bottom and sides of the Dutch oven to remove any browned bits, and cook for another 3 minutes.
Nestle the seared chuck roast back into the center of the Dutch oven.
Add the beef stock, pinch of salt, thyme, rosemary, bay leaves, and peppercorns.
Bring the mixture to a boil, then remove from the heat, cover, and transfer to the preheated oven.
Cook until the roast is tender and shreds easily with two forks, about 3-4 hours, with an interior temperature of 200-210˚F (93-100˚C).
Discard the woody stems of the herbs and the bay leaves. Season with more salt and pepper, if needed, and serve hot with desired accompaniments.