In a heavy 5-quart saucepan, melt butter over medium heat. Then add chicken and onion and cook 5 minutes or until chicken is no longer pink. (I use cooked chicken and just heat it up together.)
Add chicken broth and heat to boiling.
Stir in uncooked pasta and vegetables. Stir to coat evenly with liquid.
Heat to boiling; reduce heat. Cover; simmer on medium heat 8 minutes, stirring occasionally, or until most liquid is absorbed.
Meanwhile, in medium bowl, stir together soup, milk and 1/2 cup cheese until smooth. Stir into pasta mixture.
Simmer until heated through.
Serve sprinkled with remaining cheese.