Remove the shells and veins from the shrimp, then finely chop.
Finely chop the onion and carrot.
In a bowl, combine chopped shrimp, onion, carrot, breadcrumbs, egg, salt, and pepper.
Shape the mixture into round patties, then cook both sides in a pan with oil until golden brown.
Slice the bun in half and lightly toast it in a pan.
Layer sauce, lettuce, shrimp patty, cheese, and tomato on the bun, then close.