Prepare the Shrimp - Chop the shrimp until it turns into a chunky paste. For a quicker alternative, pulse the shrimp in a food processor.
Make the Filling - In a medium bowl, combine chopped shrimp, chives, ginger, garlic, cornstarch, soy sauce, sesame oil, salt, sugar, and pepper. Cover and refrigerate until ready to fill.
Prepare the Wrappers - If you purchased square wonton wrappers, use a 3 1/2-inch round cutter to cut out a circle shape. Keep the wrappers covered with a damp paper towel or plastic wrap to prevent them from drying out.
Shape the Dumplings - Lightly brush the edges of 1 wrapper with water. Add about 2 teaspoons of filling to center the wrapper (do not overfill). Fold the dough into a half-moon shape, remove any air, and press the edges together. Brush the outer edge of the dumpling with water. Starting on one side and then working to the other, create about 5 to 6 small pleats along the edges of the dumpling. Make sure to press the pleats to ensure that it is sealed well. Repeat with the remaining wrappers and filling.
Pan-Fry the Dumplings - Heat a large nonstick pan over medium heat. Add 1 tablespoon of the oil. Carefully add 15 dumplings to the pan. Fry until the bottoms are golden brown, about 1 to 2 minutes.
Steam the Dumplings - Reduce the heat to medium-low. Very carefully, pour in 1/4 cup water into the side of the pan. Immediately cover, allowing dumplings to steam until the water evaporates, about 3 minutes. Add more water if needed to cook the filling. Remove the lid and turn up the heat to medium. Fry until bottoms are brown and crisp, about 1 to 2 minutes. Repeat with the remaining dumplings, adding the remaining 1 tablespoon of oil for browning and then 1/4 cup water for steaming.
To Serve - Serve the dumplings hot, with your favorite dipping sauce like soy sauce, sweet and sour, or spicy chili.
Notes
Wrapper Alternatives: If you can’t find 3 1/2-inch wonton wrappers, 3-inch ones will do, but you’ll need to use only 1 teaspoon of filling per wrapper. Or use egg roll wrappers and cut them into 3 1/2-inch circles.
Make-Ahead Tips: Uncooked dumplings can be stored in an airtight container and frozen for up to 3 months. Pan-fry from frozen, adding more water if needed for steaming to cook the filling.
Storing:Store cooked dumplings in an airtight container in the refrigerator for up to 3 days.