In the work bowl of a food processor, place water chestnuts and ginger; pulse until finely minced. Scrape sides of bowl, and add shrimp, green onion, egg, cold butter, salt, and sesame seed oil; pulse until a paste consistency is reached with a few pieces remaining. Spread 1 tablespoon shrimp paste onto each bread slice, and cut in half diagonally.

In a small nonstick skillet, heat 2 tablespoons vegetable oil over medium heat. Carefully place two triangles in skillet, shrimp side down; fry until golden brown, 1½ to 2 minutes per side. Repeat with remaining 2 tablespoons vegetable oil and remaining shrimp triangles. Let drain on paper towels. Garnish with sesame seeds and green onion, if desired. Serve warm with Sweet Chili Sauce.