Place chicken, ham and broth in a 2-quart saucepan. Cover and bring to a boil. Reduce heat and simmer until chicken is tender and reaches 165 degrees. Remove cooked chicken, and ham, set aside.
Add noodles to broth. Cover and return to a boil. Reduce heat to medium and cook about 10 to 12 minutes until noodles are cooked but not mushy. Return chicken and ham to the pan. Add mustard and basil.
In a bowl whisk together milk, cornstarch, salt and pepper. Whisk into soup mixture. Bring soup to a boil over medium heat, stirring constantly. Add cheese and continue whisking over medium heat until soup reaches desired consistency.