Potstickers: In a food processor, add the shrimp, garlic, scallions, soy sauce and egg. Pulse until combined but still chunky. Remove the mixture to a bowl. To assemble the potstickers, put about 1 teaspoon of filling into the center of a wonton wrapper. Moisten the rim of the wrapper with water. Fold the dough until the ends meet and press the air out of the center towards the edges. Seal by pressing firmly. This is the simplest way.
To make the classic pleated look: using your thumb and index finger, pinch the corner of the unsealed wonton closed. Using your other hand pull a bit of the unsealed wonton edge toward the pinched corner and pinch to make a slight pleat in the wrapper, continue to pull the loose wrapper in and pleating until you run out of space, then push the air out through the final opening and pinch together. Repeat for the rest of the wontons. You can freeze them at this point on a baking sheet first, and then transfer to a freezer bag.
Dipping sauce: Stir all the ingredients together in a small serving bowl.
When ready to cook the potstickers, add oil to a large saute pan. When oil begins to swirl, add potstickers to the pan and cook until golden brown on 1 side. Flip and add 3 ice cubes. Immediately cover the pan to let the potstickers steam and cook through, about 3 minutes. Remove to a large platter and serve with dipping sauce.