Heat oven to 400°F. Place 8 (10-oz) ramekins or custard cups on large cookie sheet with sides. In 3-quart saucepan, heat chicken, thawed vegetables, pasta sauce and milk over medium heat, stirring occasionally, until thoroughly heated. Spoon mixture into ramekins.
Sprinkle cheese on plate. Unroll dough. Separate 1 strip at a time; press both sides into cheese. Twist strip; arrange on mixture in ramekin in loose spiral shape, beginning at outside and coiling toward center. Repeat with remaining strips of dough and cheese. Sprinkle any remaining cheese over dough.
Bake 15 minutes. Cover ramekins loosely with sheet of foil; bake about 12 minutes longer or until filling is hot and bubbly.