Preheat oven to 400°F. Place vegetables in a sieve or colander. Run cold water over vegetables to thaw. Separate breadsticks into 12 pieces; set aside.
In a plastic bag combine flour, sage, salt, and pepper. Add chicken pieces, about one-fourth at a time, shaking to coat. In a large skillet heat oil over medium-high heat. Add chicken; sprinkle with any remaining flour mixture. Cook and stir about 2 minutes or until brown. Add broth, milk, and vegetables. Bring to boiling, stirring once.
Divide chicken mixture among four 16-ounce au gratin dishes or individual casseroles. Arrange three breadsticks across the top of each dish. Sprinkle with cheese. Bake about 18 minutes or until breadsticks are browned and filling is bubbly.