In a large bowl, mix the ground pork, shrimp, oyster sauce, white pepper, and sesame oil.
Using a knife, snip off a little bit of each corner of the won ton skins to make the skins more circular.
Using a teaspoon, coat the back of the spoon with the egg mixture, and use the spoon to brush one won ton skin. Get a scoop of the meat mixture with the teaspoon to fill the won ton. Shape the won ton around the meat mixture, but do not close off the skin. The sui mai should be cyclindrical (flat on the bottom and top, but with the meat exposed on the top). Continue to make the rest of your sui mai.
Once they are all made, oil the middle layer of a large Chinese steamer. Place the sui mai in the middle section, then top each sui mai with a piece of carrot.
Fill the bottom of the steamer with water and place on the stove. Bring the water to a boil. Once the water begins to boil, bring the heat to low. Assemble the steamer with the lid on. Steam for 20 minutes, or until the sui mai are cooked throughout.
