Preheat the oven to 450ºF. In a medium saucepan, bring 1 ½ quarts water to a simmer. Add the bacon and cook for 10 minutes; drain and dry on paper towels.
In a large dutch oven, heat the oil over medium heat. Add the bacon and sauté for 2-3 minutes or until lightly browned. Remove the bacon with a slotted spoon; set aside in a medium bowl. Working with a few pieces at a time, sauté the beef in the hot bacon fat until lightly browned on all sides. Add the beef to the bacon. In the same fat, add the carrot and onion until lightly browned, about 5-7 minutes. Add the vegetables to the bacon and beef; pour out the cooking fat from the dutch oven.
Return the beef, bacon, and vegetables to the dutch oven and toss with salt and pepper. Sprinkle in the the flour and toss to coat the beef lightly with the flour. Place the pot in the oven and cook for 4 minutes. Carefully remove the pot from the oven, toss the meat, and return the pot to the oven for 4 minutes more. (This browns the flour and covers the meat with a light crust.) Remove the casserole and turn the oven temperature to 325ºF. Set the rack in the lower third of the oven
Add the wine and enough stock to cover the meat. Add the tomato paste, garlic, and herbs. Bring the mixture to a simmer. Cover and set in the oven. Regulate the heat so the mixture simmers slowly for 2 ½ to 3 hours. The meat is done when a fork pierces it easily.
When the meat is tender, remove the beef and bacon and strain the liquid; discard the carrot and onion. Clean out the Dutch oven and return the beef and bacon to it. Skim the fat from the sauce and return it to the pot with the beef and bacon. Add the carrots and cook until the carrots are tender, about 35-40 minutes. Using a slotted spoon, transfer the carrots and meat to a serving platter.
In a small bowl, mix together the butter and flour to form a paste. Add the kneaded butter to the sauce and cook just until the sauce has thickened. Pour the sauce over the meat and serve with the Brown Braised Pearl Onions and Sautéed Mushrooms (recipes follow). The beef, vegetables, and sauce can be made one day in advance (refrigerate the onions and mushrooms separately). Leftovers can be stored in an airtight container for 3 days. Enjoy!