Finely chop the green onions and mince the garlic. In a mixing bowl, combine the shrimp, garlic, ginger, green onions, salt, and pepper. Let this mixture marinate for about 15 minutes.

Heat a deep pan over medium heat with enough oil for frying (about 2-3 inches deep). Setup wonton wrappers on a clean surface. Place a spoonful of shrimp filling at the center of each wrapper. Brush the edges with beaten egg and fold to seal, pressing out any air.

Gently lower a few wontons into the hot oil, frying for 3 to 4 minutes until golden brown. Use a slotted spoon to remove them and drain on a paper towel-lined plate.

Arrange the fried wonton-wrapped shrimp on a platter and serve hot with dipping sauces like sweet chili or soy sauce.