1. Melt butter in a large saucepan over medium heat. Add onion; cook 5 minutes, stirring occasionally. Add broth, potato and carrots; bring to a boil over high heat. Reduce heat; simmer uncovered 5 minutes.
  2. Add broccoli, salt and pepper; cook 5 minutes.
  3. Place flour in a medium bowl. Gradually stir in milk, mixing well.
  4. Add milk mixture and cooked chicken to soup; bring to a simmer. Simmer uncovered 5 minutes or until vegetables are tender and soup has thickened.