Pulse shrimp, chili paste, lemongrass, fish sauce, and ginger in a food processor until smooth. Season with salt and pulse again to combine. Transfer mixture to a medium bowl; stir in scallion whites. Place sesame seeds on a plate. Spread shrimp mixture over bread slices, extending all the way to edges. Press bread, shrimp side down, into sesame seeds to coat evenly. Pour oil into a large skillet to come 1/4″ up sides and heat over medium-high until a small pinch of shrimp mixture sizzles when added to oil. Working in 2 batches, fry toasts, shrimp side down, until golden and crisp, about 2 minutes; turn and cook until other sides are golden and crisp, about 1 minute. Transfer to a paper towellined wire rack to drain. Cut each toast diagonally into quarters and top with scallion greens.