Make the shrimp topping. In a food processor, pulse together the scallions, cilantro, and garlic until well-chopped. Add the egg white, soy sauce, toasted sesame oil, salt, black pepper, ground ginger, and ¾ of the shrimp. Pulse until a paste forms. Transfer the mixture to a mixing bowl, finely chop the rest of the shrimp, and fold it into the mixture.
Assemble. Spread the shrimp mixture evenly over each piece of bread and sprinkle each slice with sesame seeds. Press the sesame seeds into the bread.
Fry. In a large, heavy-bottomed pan, heat about 1/8-inch of vegetable oil over medium-high heat. Wait for the oil to shimmer before adding the shrimp toast to the pan, shrimp side down. Fry for 2 minutes, flip, and fry for an additional 1 minute. Do not crowd the pan. Fry the toasts in batches if necessary.
Remove from the pan and set aside on a paper towel-lined plate while you work on the rest of the toasts.
Serve. Cut each slice into quarters and serve warm.