In a bowl, mix pork, shrimp, green onions, ginger, rice wine, and soy sauce.
On a flat, clean surface, lay out gyoza wrappers. Top each with about 1 tbsp. pork-shrimp mixture. Brush edges of wrapper with beaten egg and form dumplings. Put shu mai in parchment-lined steamers (see â€œHow to Steam Dim Sum,â€� below).
Steam dumplings until cooked through, about 10 minutes. Serve immediately.
How to Steam Dim Sum: Measure your steamer basket and choose a pot with a diameter at least 2 in. wider. To keep dumplings from sticking, cut a circle of parchment paper 1 in. smaller in diameter than the basket (so steam can flow up around the edges) and fit it in. Pour enough water into pot to come 1 in. up side and bring to a boil over high heat. Fill basket with dim sum first, then set it in the pot. Cover and cook, adding hot water as needed.
Note: Nutritional analysis is per dumpling.