Mix 2 tablespoons of flour with 1 teaspoon of salt and pepper in a large bowl. Toss the beef cubes in the mixture until evenly coated.
Heat 2 tablespoons of vegetable oil in a heavy-bottomed pot or Dutch oven over medium-high heat. Brown the beef in batches, ensuring not to overcrowd the pan. Cook each batch for about 5 minutes, turning to brown all sides. Remove the beef and set it aside.
Add the onion, carrots, and celery to the pot. Sauté for 3–4 minutes until the onion softens slightly. Add the garlic and cook for another minute. Remove the vegetables from the pot and set aside.
Reduce the heat to medium and pour in the red wine and red wine vinegar. Scrape up any browned bits from the bottom of the pot with a wooden spoon to release their flavor.
Return the browned beef to the pot. Add the beef broth, bay leaves, and thyme. Bring the mixture to a boil, then reduce the heat to low and cover. Simmer gently for 1½ hours, skimming off any foam or fat that rises to the surface.
Add the sautéed vegetables and potatoes to the pot. Simmer for an additional 15–20 minutes, or until the potatoes are fork-tender and the vegetables are cooked through.
Mix the remaining 2 tablespoons of flour with 3 tablespoons of water to create a slurry. Stir it into the stew and bring to a gentle boil, letting it thicken for 3–4 minutes. Adjust the seasoning with additional salt and pepper, as needed.
Ladle the stew into bowls and serve hot with your favorite sides.