In a large mixing bowl, combine the ground pork, chopped shrimp, soy sauce, sesame oil, minced ginger, minced garlic, and green onion. Season with salt and pepper to taste. Mix well until fully combined.
Take a wonton wrapper and place about 1 tablespoon of the filling in the center. Moisten the edges with a little water. Fold the wrapper in half to form a triangle, pressing to seal. Then, bring the two corners of the triangle together and pinch to seal, forming a wonton. Repeat with remaining wrappers and filling.
In a large pot, bring the chicken broth to a boil. Add the soy sauce, sesame oil, and minced ginger.
Carefully drop the wontons into the boiling broth. Cook for about 5-7 minutes or until they float to the top and are cooked through.
Once cooked, use a slotted spoon to remove the wontons and divide them among serving bowls. Ladle the hot broth over the wontons.
Garnish with chopped green onions and fresh cilantro if desired. Serve hot.
You can prepare the wontons in advance and freeze them. Just add them directly to the boiling broth without thawing.
For a spicier broth, add some chili oil or sliced jalapeƱos to serve.