Mix the ground beef with the garlic, ginger, egg and green onions and use your bare hands to combine everything. Mix the sesame oil, soy sauce, salt and pepper together and pour this into the beef mixture. Mix well. Lay out the wonton wrappers and divide the beef mixture between them (you can do them one by one, using about a tablespoon of filling in each, or lay them all out if you have a big work surface).
Dip your finger in water and trace along half the wonton wrapper edge, folding the wrapper over to make a triangle and pressing the edges shut, squeezing out any excess air as you go.
Steam the wontons for 8 minutes in batches or until the inside is cooked through (you will have to open one to check). If you are freezing them and then cooking them from frozen, they will need an additional 5 minutes in the steamer. These wontons can also be poached (cook them in simmering water until they float to the surface).