In a mixing bowl, combine the ground pork or shrimp with minced garlic, minced ginger, chopped green onions, soy sauce, and sesame oil. Mix until well blended and slightly sticky.

Take a wonton wrapper and place about 1 teaspoon of the filling in its center. Wet the edges of the wrapper, then fold to create a triangle and press the edges together to seal.

In a large pot, pour in 2 cups of broth and bring it to a gentle boil over medium heat. Let simmer for about 5 minutes.

Carefully add the assembled wontons to the boiling broth. Stir gently to prevent sticking and cook for about 4-5 minutes until they float.

Ladle the soup into bowls, ensuring each has an even number of wontons, and sprinkle with extra chopped green onions for garnish.