In a large bowl, combine ground pork, green onions, garlic, soy sauce, sesame oil, ginger, white pepper, and cornstarch. Mix until well combined.
Form the mixture into small meatballs, about 1-inch in diameter, and set aside.
In a large pot, bring the chicken broth, sliced ginger, green onions and carrots to a boil.
Gently add the meatballs to the pot and cook for about 10-15 minutes, until they're cooked through and float to the surface.
Gently stir in the wonton wrapper pieces. Let them cook for 2-3 minutes until tender.
Taste the soup and adjust seasoning with salt, pepper, or additional soy sauce if needed.
Remove the ginger and green onions, if you wish. Season the soup with the soy sauce, sesame oil, and salt to taste.
Ladle the soup into bowls and garnish with sliced green onions, fresh cilantro, and a drizzle of chili oil if desired.