Add 1 tablespoon vegetable oil to a wok over high heat. Add the garlic and ground chicken. Cook for 1 minute, then add shaoxing wine. Break up the chicken finely.

Add in the mushrooms, soy sauce, oyster sauce, sesame oil, and water. Cook, stir often until softened.

Add green onions on top and let it cool.

Bring a saucepan filled with water to a boil. Fill a large bowl with ice water and place next to the saucepan. Add the reserved green parts of the onions to the boiling water, making sure they completely submerge. Blanch for 30 seconds, then immediately transfer to ice water. Remove once they are cool enough to handle and lightly pat to dry. Use a knife to split each blade in half lengthwise or quarters if large.

Place a wonton wrapper on a dry work surface. Put a 1 tsp of the cooled filling in the center of the wrapper. Moisten the edges with water and gather together over the filling. Pinch together to seal and lightly form the bottom so it is rounded. Tie one of the blanched green onion blades around the pinched area of the dumpling and double tie to secure. Trim off the ends. Repeat with remaining wrappers.

Add oil into a wok until it is 3 inches deep. Heat it to 325 degrees F. Fry the dumplings until golden brown, then transfer to a towel-lined plate. Repeat with remaining dumplings.