Wash the carrot thoroughly and julienne it finely.
Mix the julienned carrots with sugar, salt, lemon juice, and olive oil until well combined.
Spread butter on slices of bread or a baguette and add sliced cheese.
Generously top with the prepared carrot râpée.
Add ham, arugula, or other toppings as desired.
Cover with another slice of bread to complete the sandwich.