In a mixing bowl, combine ground beef, finely chopped raw shrimp, grated fresh ginger, and finely chopped green onions. Add light soy sauce, Chinese cooking vinegar, salt, and toasted sesame oil. Mix thoroughly until sticky, then knead for 3-5 minutes until it holds its shape.

Take a wonton wrapper and place 1 to 1.5 teaspoons of the filling in the center. Moisten the edges with water, then fold the wrapper diagonally to create a triangle shape. Press the edges firmly to eliminate air bubbles.

In a large pot, pour in chicken broth and add smashed garlic cloves, a slice of fresh ginger, light soy sauce, sugar, and Chinese cooking vinegar. Heat over medium heat, bringing the broth to a gentle simmer. Allow it to blend for 10-15 minutes, then adjust seasoning as needed.

In a separate large pot, bring salted water to a rolling boil. Drop the wontons in batches into the boiling water. Cook for 3-5 minutes, or until they float, then simmer for an additional minute before removing.

While the wontons are cooking, reheat your aromatic broth on low heat. Use a slotted spoon to transfer the cooked wontons into serving bowls, then ladle the hot broth over them. Garnish with reserved green onion tops or a drizzle of sesame oil.