Mix meat with the scallions, soy sauce, white pepper, sesame oil, and 1/2 the beaten egg. Reserve the other 1/2 egg to seal the dumplings
In a small sauce dish, combine ingredients for the dipping sauce
Arrange several wonton wrappers with corners facing you. Place 1/2 tablespoon of meat mix in the center of each wrapper. Use a pastry brush or fingers to brush edges with beaten egg. Fold wrapper in half and form into dumplings. Repeat.
Steam for 5-6 minutes (grease steamer basket with cooking oil if using a metal steamer).