Divide stew meat, onions and celery among several large kettles. Add water to fill kettles half full. Add browning sauce if desired and seasonings.
Bring to a boil. Reduce heat; cover and simmer for 1-1/2 hours or until the meat is tender. Add potatoes and carrots; bring to a boil. Reduce heat; cover and simmer for 40 minutes or until vegetables are tender.
Add peas and corn; bring to a boil. Reduce heat; simmer, uncovered, for 1 hour.
Combine flour and enough milk to achieve a creamy, smooth paste; gradually add to stew. Bring to a boil. Cook and stir for 2 minutes or until thickened. Discard bay leaves. Yield: 120 (1-cup) servings.