Arrange broccoli in a vegetable steamer over boiling water. Cover and steam 3 minutes or until crisp-tender. Set aside.
Combine chicken, Cheddar cheese, and cream cheese in a small bowl, stirring well. Add broccoli, chicken broth, and next 3 ingredients; stir well. Place 1 sheet of phyllo on a damp towel (keeping remaining phyllo covered). Lightly coat phyllo with cooking spray; fold phyllo in half crosswise, bringing short ends together. Lightly coat with cooking spray. Spoon half of chicken mixture onto narrow end of phyllo; fold over lengthwise edges of phyllo to partially enclose filling. Fold narrow end of phyllo over mixture, and roll up, jellyroll fashion. Repeat procedure with remaining phyllo and chicken mixture.
Place phyllo packets, seam side down, on a baking sheet coated with cooking spray. Lightly coat tops of packets with cooking spray. Bake at 350° for 20 to 25 minutes or until golden.