Make the wontons: Mix pork, shrimp, rice wine, soy sauce, brown sugar, green onions, and ginger together in a large bowl until well combined. Let stand for 25 to 30 minutes.
Spoon about 1 teaspoon filling onto the center of a wonton wrapper. Moisten all four wrapper edges with water and fold over filling to make a triangle; press the edges firmly to seal. Bring left and right corners together above filling; overlap the tips of these corners, moisten with water, and press together to seal. Repeat until all wrappers have been filled and sealed.
Make the soup: Bring chicken stock to a rolling boil in a pot. Gently drop in wontons and cook for 5 minutes.
Ladle into bowls and garnish with green onions.
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To Fry Wontons:
Heat 2 to 3 cups oil in a wok until hot. Deep-fry wontons in batches in hot oil until golden, 2 to 3 minutes per side. Drain on a paper towel-lined plate. Serve with duck sauce (plum sauce) or any dipping sauce.
Recipe Tip
Uncooked wontons keep in the freezer for up to 2 months if they're wrapped well. Thaw them first if you're frying them, but if you're boiling them, drop frozen wontons into boiling broth and cook for 7 minutes.
