Place first 7 ingredients in a food processor; add 1/2 teaspoon salt. Pulse until coarsely chopped.
Working with 1 wonton wrapper at a time (cover remaining wrappers with a damp towel to prevent drying), spoon about 1 teaspoon chicken mixture into center of each wrapper. Moisten edges of wrapper with egg white; bring 2 opposite corners to center, pinching points to seal. Bring remaining 2 corners to center, pinching points to seal. Pinch 4 edges together to seal. Place wonton on a baking sheet sprinkled with cornstarch. Repeat procedure with remaining wrappers, chicken mixture, and egg white. Refrigerate 20 minutes.
Bring stock to a simmer over medium heat; add 1/2 teaspoon salt. Add wontons; cook 4 minutes or until wontons float to the top, stirring gently. Sprinkle with crushed red pepper, if desired.