In a small skillet, heat the vegetable oil over medium heat. Soften the ginger, garlic and scallion. Remove from heat and add soy sauce to cool down.
In a medium mixing bowl, add the ground chicken, ground pork, garlic and scallion mixture, Kikkoman® Sesame Oil and white pepper. Mix until fully incorporated.
Spoon 1/2 tablespoon of mixture onto the top half of wonton skin and fold into a rectangle, sealing edges with a finger dipped in water. Join the two bottom edges together and seal with water. Repeat with remaining wonton skins.
In a 4-quart saucepan, bring water to a boil. Add dumplings and boil for about 2 minutes, until they float to the top. Remove dumplings with a spider, reserving 1/4 cup of dumpling water.