In a food processor, pulse the shrimp until coarsely chopped. Be careful not to over-process; you want some texture.
In a large bowl, combine the chopped shrimp, breadcrumbs, green onions, cilantro, garlic, ginger, egg, soy sauce, sesame oil, salt, and black pepper. Mix until well combined.
Form the mixture into small balls, about 1 inch in diameter.
Heat about 2 inches of vegetable oil in a deep pot over medium heat until it reaches 350°F.
Carefully add the shrimp balls to the hot oil in batches, frying for about 3-4 minutes or until golden brown and cooked through. Use a slotted spoon to remove them and drain on paper towels.
Serve warm with your favorite dipping sauce.