Start by washing and drying the cucumber and carrots thoroughly. Use a sharp knife or a julienne peeler to cut the cucumber into thin strips, ensuring they maintain a firm texture.

In a small bowl, combine the olive oil, fresh lemon juice, gochugaru, soy sauce, and sugar. Use a whisk to mix the ingredients until they are well blended, and the sugar has dissolved.

In a large mixing bowl, add the julienned cucumbers and carrots you prepared earlier. Pour the freshly whisked dressing over the vegetables.

Incorporate the minced garlic and finely chopped parsley into the bowl with the cucumber and carrot mixture. Gently toss everything together until all the vegetables are evenly coated.

Sprinkle sesame seeds over the top of the salad. Serve immediately, or let it sit for 10-15 minutes to meld the flavors before enjoying.