In a large pot combine broth and potatoes. Cover and simmer for 10 minutes. Add carrots and celery; cook 5 minutes. Add broccoli and simmer another five minutes.
In a saucepan, melt butter and stir in flour. Gradually add milk, stirring constantly, add 1 cup of broth from the soup. Cook on low heat until slightly thickened; blend into rest of the soup. Heat to serving temperature but do not boil. Season with salt and pepper to taste. Makes 6-8 servings.