In a large pot over medium heat, add sesame oil.
Add ginger and garlic, stirring constantly and cook for 1 minute.
Pour in chicken broth and water, stirring to combine.
Add soy sauce, rice vinegar, salt, and white pepper. Bring the mixture to a boil.
Once boiling, carefully add the frozen wontons. Stir gently to separate them.
Reduce heat to a simmer and cook until the wontons float and the wrappers are fully cooked through, about 4 to 6 minutes.
Ladle soup into bowls and serve hot garnished with green onions.