In a bowl, combine ground pork, shrimp, garlic, green onions, soy sauce, oyster sauce, sesame oil, white pepper, and the egg until well mixed.
Place a wonton wrapper in your palm and spoon about 1 teaspoon of filling into the center.
Gather the edges up around the filling and gently press to seal, leaving the top open.
Repeat with the remaining wrappers and filling.
Arrange the dumplings in a steamer lined with parchment paper or cabbage leaves to prevent sticking.
Steam over boiling water for 10–12 minutes until fully cooked.
Garnish with grated carrot if desired and serve with your favorite dipping sauce.