Put the shrimp, egg white, onions, cilantro, salt, cayenne, and 1/2 teaspoon of the sesame oil in a food processor and pulse 2 or 3 times to finely chop. Do not puree. Put the egg yolks, the remaining 2 tablespoons sesame oil and the water in a shallow bowl and whisk to blend.
Spread equal amounts of the shrimp mixture onto 8 slices of the bread. Top with the remaining slices of the bread. Press together gently but firmly.
Heat 3 tablespoons of the vegetable oil in a large nonstick skillet over medium high heat. Dip 4 of the sandwiches in the egg mixture, coating them evenly on both sides. Fry until golden brown, about 4 minutes on each side. Remove from the skillet. Repeat the process with the remaining 3 tablespoons vegetable oil and sandwiches.
Slice each sandwich into 4 triangles, place on a serving plate and garnish with parsley.