Preheat oven to 350 degrees. In a Dutch oven (5-quart) with a tight-fitting lid, combine beef, tomato paste, vinegar, and flour; season with salt and pepper.
Add onions, potatoes, carrots, garlic, bay leaves, and 3 cups water. Bring to a boil. Cover, transfer to oven, and cook until meat is fork-tender, 2 to 2 1/2 hours. Remove bay leaves and, if desired, season with salt and pepper before serving.
Slow-Cooker Variation: Place beef in a 5-quart slow cooker. Distribute tomato paste, vinegar, and flour over beef; season generously with salt and pepper. Add onions, potatoes, carrots, garlic, and bay leaves. Cover slow cooker; cook on high until beef is fork-tender, about 5 hours (or cook on low heat 8 hours).