Make the shrimp paste: Process the egg white, ginger, garlic, 1 tablespoon of the soy sauce, 1 tablespoon of the sesame oil, the sherry, 3/4 teaspoon salt, 1/2 teaspoon of the brown sugar and several grinds of pepper in a food processor until all the ginger and garlic are pureed. Add the shrimp, and pulse until a thick paste forms. Transfer to a medium bowl, and fold in 2/3 of the scallions, the celery, water chestnuts and sesame seeds. (The shrimp paste can be refrigerated for up to 1 day.)
Trim the crusts from the bread, and evenly divide the shrimp paste among the slices (about 2 heaping tablespoons each). Spread out into an even layer that completely covers the bread.
Make the dipping sauce: Whisk together the remaining 2 tablespoons soy sauce, 1 teaspoon sesame oil and 1 teaspoon brown sugar, the lemon juice and a large pinch of salt in a small bowl.
Fry the toasts: Line a baking sheet with paper towels. Fill a large, wide skillet with straight sides, with about 1 inch of vegetable oil. Attach a deep-fry thermometer to the skillet, and bring the oil to 375 degrees F over medium heat. Being careful of the hot oil splashing, put 5 to 6 shrimp toasts in the oil shrimp-side down and fry until the shrimp and the edges of the bread are golden brown, 2 to 3 minutes. Flip the pieces, and continue to fry until the bottoms are golden brown, about 1 minute more. (Adjust the heat as needed to maintain the temperature.) Transfer the shrimp toasts to the prepared baking sheet, and dab the tops with a paper towel to absorb some of the excess oil. Sprinkle the toasts all over with the remaining scallions and some sesame seeds and salt. Cut each toast into 4 triangles, and serve hot with the dipping sauce on the side.
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