Asiago cheese in the chicken dumplings adds an Italian touch to wonton soup.
Stir chicken, cheese, chopped parsley, 1/2 teaspoon salt, 1/4 teaspoon pepper, and eggs in bowl and set aside.
Roll out 2 wonton wrappers on a lightly floured surface to 4 1/2-inch squares. Place a tablespoon of chicken filling in center of a wrapper. Place 1 parsley leaf on top of filling. Moisten edges of wrapper with water and a wet pastry brush. Top with other wrapper. Press edges with fork tines to seal. Repeat to make 8 ravioli.
Bring chicken stock to a simmer in a large pot. Season the chicken stock with salt and pepper to taste. Add the ravioli, one at a time, and cook 2 minutes. Divide stock and ravioli evenly between 4 serving bowls (8 serving bowls if serving as a first course).