Wash and peel the carrot into thin ribbons using a peeler. Place the carrots in a bowl and sprinkle with salt. Mix and set aside for 10 minutes.
Mix ingredients for dressing and pour on carrots. Stir to distribute evenly.
Add oil to a pan and fry the eggs.
Lightly toast bread slices. Spread mayonnaise on two slices, and whole grain mustard on the others.
Assemble sandwiches in the following order: mustard toast, lettuce, fried egg, carrot salad, mayonnaise toast.
Tightly wrap sandwiches in a sandwich wrap to compress the carrots. Slice sandwiches in half and enjoy!