Add the cilantro stems, the whites from the green onions, garlic, shrimp, egg white, cornstarch, fish sauce and salt to the bowl of a food processor fitted with the blade attachment. Pulse until ground.
Mound about 2 tablespoons of the shrimp egg paste high in the center of each slice of bread and spread it evenly to corners with a spoon or rubber spatula.
If using sesame seeds, add them to a shallow dish or plate and spread out. Dip each slice of the shrimp-topped toast, shrimp-side down onto the sesame seeds.
Fill a large cast iron pan or Dutch oven with enough oil to reach 1” up the side of the pan. Heat the oil to 350ºF (177ºC).
Working with two slices of bread at a time (if the size of the pan allows), place slices of bread, shrimp-side down, into the hot oil. Fry until the undersides are light gold in color, about 3 minutes.
Flip the toasts and continue to cook until fried to a golden brown, about an additional 2 minutes. Remove from the oil to a wire rack set over a baking sheet.
Cut each slice on the diagonal to create 4 equal triangles. Repeat with the remaining ingredients until all have been fried.
Arrange shrimp toasts on a serving platter and top with the remaining green onions, sliced on the bias. Serve on their own or drizzled with sriracha and mayonnaise.