These open-faced dumplings (pronounced "shoe-MY") are made with round gyoza skins. If you can't find gyoza skins, purchase wonton wrappers instead, and cut them into circles with a three-inch round biscuit cutter. You can make and refrigerate the seafood-and-vegetable filling up to a day in advance; fill and steam the dumplings shortly before serving them. If you don't have a bamboo steamer, prepare these in two or three batches in a collapsible metal steamer basket (be sure to line it with lettuce leaves so that the dumplings don't stick).
1/3 cup chopped shiitake mushroom caps
1/3 cup chopped water chestnuts
3 tablespoons chopped green onions
2 garlic cloves, chopped
1 teaspoon grated peeled fresh ginger
1/2 teaspoon dark sesame oil
1/4 teaspoon salt
5 ounces sea scallops, chopped
1 (6-ounce) can lump crabmeat, drained (such as Chicken of the Sea)
To prepare dumplings, place first 4 ingredients in a food processor; pulse 8 times or until finely chopped. Add ginger, oil, salt, and scallops; pulse 4 times or until scallops are finely chopped. Spoon mixture into a medium bowl; add crabmeat and egg, tossing to combine.
Working with 1 gyoza skin at a time (cover remaining skins to prevent drying), spoon about 1 tablespoon filling into center of each skin. Gather up edges of skin around filling; lightly squeeze skin to adhere to filling, leaving top of dumpling open. Smooth surface of filling with the back of a spoon dipped in water. Place dumplings on a baking sheet sprinkled with cornstarch; cover loosely with a damp towel to prevent drying.
Line each tier of a 2-tiered (10-inch) bamboo steamer with 4 of the lettuce leaves. Arrange 9 dumplings, 1 inch apart, over lettuce in each steamer basket. Stack tiers, and cover with the steamer lid. Add water to a large skillet to a depth of 1 inch; bring to a boil. Place steamer in pan; steam dumplings 10 minutes. Remove dumplings from steamer.
To prepare sauce, combine sugar and remaining ingredients, stirring with a whisk until sugar dissolves. Serve sauce with dumplings.