1. Cook edamame according to package directions; drain. Rinse under cold water; drain.
2. Combine cornstarch and next 8 ingredients (through egg white) in the bowl of a food processor; pulse until finely chopped. Combine edamame, shrimp mixture, and cabbage in a bowl. Refrigerate mixture 10 minutes.
3. Combine 1 tablespoon hot water and brown sugar in a bowl, stirring until brown sugar dissolves. Stir in lime juice, chili garlic sauce, and fish sauce.
4. Working with 1 wonton wrapper at a time (cover remaining wrappers to keep them from drying), moisten outside edge of wrapper with water. Spoon about 1 1/2 teaspoons shrimp mixture into center of circle. Fold wrapper over filling; pinch edges together to seal. Repeat procedure with remaining wrappers and shrimp mixture (cover formed dumplings to keep them from drying).
5. Heat a large skillet over high heat. Coat pan with cooking spray. Arrange 12 dumplings in pan; cook 1 minute. Turn dumplings over. Carefully add 1/4 cup water to pan; cover immediately. Cook 2 minutes; place cooked dumplings on a platter. Wipe pan with a paper towel. Repeat procedure with cooking spray, remaining 12 dumplings, and remaining 1/4 cup water. Serve immediately with sauce.