Trim fat from meat; sprinkle with salt and pepper. In 6- to 8-quart Dutch oven brown beef in hot oil over medium heat. Drain off fat; discard. Add onions, broth, and wine.
Bring mixture to boiling; reduce heat. Simmer, covered, 1 hour. Add whole potatoes. Return to boiling; reduce heat. Simmer, covered, 45 minutes. Add carrots. Cover; cook 30 minutes or until meat and vegetables are tender, spooning juices over meat and vegetables twice during cooking.
Using slotted spoon, transfer meat and vegetables to serving platter. Skim fat from juices. If necessary, add water to juices to equal 1-12 cups. Return juices to pan. In screw-top jar combine the cup water and flour. Cover; shake to combine. Add to juices in pan. Cook and stir over medium heat until thickened; cook and stir 1 minute more. Season with salt and pepper. Spoon over meat and vegetables. Makes 6 servings.