In a bowl, combine flour, about 1/2 teaspoon salt, and 1/4 teaspoon pepper. Add beef and dredge in flour mixture.
In a Dutch oven over medium-high heat, heat 2 tablespoons of the oil.
Add beef in batches and sear until browned on all sides. Remove beef from the pot and keep warm.
Add another 1 tablespoon of oil to the pot. Add onions and garlic and cook, stirring occasionally, until softened.
Add beef broth, tomato sauce, and Worcestershire sauce.
Add bay leaves. Bring to a boil.
Lower heat, cover, and simmer for about 1 1/2 to 2 hours or until meat are tender.
Remove bay leaves and discard.
Add potatoes, carrots, and celery.
Continue to cook for about 30 to 40 minutes or until meat is fork-tender and vegetables are cooked.
Season with salt and pepper to taste. Serve hot.