To make the dipping sauce: In a saucepan over medium heat, combine the water, rice vinegar, ketchup, sugar, and salt. Bring to a simmer. Stir in the cornstarch slurry and cook until the sauce thickens. Remove from the heat and set aside.
To prepare the shrimp paste: In a mixing bowl, add the minced shrimp, salt, white pepper, sesame oil, cornstarch, egg whites, ginger, and cilantro stems. Mix thoroughly until a smooth paste forms.
To assemble the shrimp toast: Trim the crusts off the sandwich bread slices. Cut each slice diagonally into two triangles. Spread a generous layer of shrimp paste onto one side of each bread triangle. Brush both sides of the toast with the whisked egg yolks. Press both sides into breadcrumbs to coat evenly.
To fry the shrimp toast: Heat the cooking oil in a deep pan over high heat to 325°F (163°C). Carefully add the shrimp toast, shrimp-side down first, and fry for about 2 minutes per side, or until golden brown. Remove and drain on a paper towel-lined plate.
To serve: Serve hot with the sweet and sour dipping sauce on the side.