Combine the flour and pepper in a bowl, add the beef and toss to coat well. Heat 3 teaspoons of the oil in a large pot. Add the beef a few pieces at a time; do not overcrowd. Cook, turning the pieces until beef is browned on all sides, about 5 minutes per batch; add more oil as needed between batches.
Sauté the onions and add 1 to 2 tablespoons of tomato paste. Continue to cook until the color starts to go from bright red to rust, then deglaze with the wine and vinegar. Ensure that any remains from cooking the beef and onions are loosened up from the bottom of the pan. Return the beef to the pot and add the beef broth and bay leaves. Bring to a boil, then reduce to a slow simmer.
Cover and cook, skimming broth from time to time, until the beef is tender (about 1.5 hours). Add the carrots, salt, pepper, and cajun seasonings, then bring to a simmer, covered, for 10 minutes. Add the potatoes and simmer until all vegetables are tender, about 30 minutes more. Add broth or water if the stew is dry. Serve and enjoy!