Place shrimp, water chestnuts, cilantro leaves, green onions, garlic, grated ginger, anchovy filet, sesame oil, fish sauce, soy sauce, egg white, sugar, paprika, cayenne pepper, and salt into the bowl of a food processor. Pulse several times; scrape down sides of bowl. Continue to process until mixture is well blended and reaches a paste consistency, 1 or 2 minutes. Transfer mixture to a bowl; cover with plastic wrap and refrigerate to blend the flavors, about 1 hour.
Very lightly toast bread slices. Trim crusts from bread. Spread shrimp paste onto bread in an equal thickness as the bread. Cut slices in half and then diagonally into diamond shapes. Sprinkle with sesame seeds.
Place a heavy skillet over medium-high heat; pour in about 1/2 inch of vegetable oil. When oil is hot, place bread slices, paste side down, into the oil. Fry until crispy, 2 to 3 minute per side. Transfer to a paper towel-lined plate. Serve hot or warm garnished with additional sliced green onions.
