To prepare sauce, combine first 4 ingredients; set aside.
To prepare wrapper, lightly spoon flour into dry measuring cups; level with a knife. Combine flour and water in a bowl. Turn dough out onto a floured surface; knead 5 minutes. Cover dough; let rest 30 minutes.
To prepare filling, heat a large non-stick skillet coated with cooking spray over medium-high heat. Add mushrooms; cook 3 minutes or until moisture evaporates, stirring frequently. Add cabbage; cook 3 minutes or until softened, stirring frequently. Stir in 2 tablespoons green onions and next 6 ingredients (2 tablespoons green onions through garlic); simmer 2 minutes. Remove from heat; set aside.
Divide dough into 4 equal portions. Roll each portion into a 1-inch-thick rope. Cut each rope into 12 equal pieces. Shape each dough piece into a ball. Roll each ball into a 4-inch circle on a floured surface (cover circles with a damp towel to prevent drying).
Working with 1 wrapper at a time, spoon 2 teaspoons mushroom mixture into center of wrapper. Fold in half. Fold top edge of wrapper at 1/2-inch intervals to form pleats, pressing against bottom edge to seal. Place dumplings, pleated sides down, on a large baking sheet dusted with flour; cover loosely with towel to prevent drying.
Line each tier of a 2-tiered (10-inch) bamboo steamer with 3 lettuce leaves. Arrange 6 dumplings, 1-inch apart, in each steamer basket. Stack tiers; cover with steamer lid. Add water to a large skillet to a depth of 1 inch; bring to a boil. Place steamer in pan, and steam dumplings 5 minutes. Remove dumplings from steamer. Repeat procedure with remaining lettuce and dumplings.
Heat 1 1/2 teaspoons oil in a large non-stick skillet over medium-high heat. Add 12 dumplings; cook 1 1/2 minutes on each side or until browned. Repeat procedure 3 times with remaining oil and dumplings. Serve with sauce.
MyRecipes is working with Let's Move!, the Partnership for a Healthier America, and USDA's MyPlate to give anyone looking for healthier options access to a trove of recipes that will help them create healthy, tasty plates. For more information about creating a healthy plate, visit www.choosemyplate.gov.