Wash and dry the cucumbers and carrots thoroughly.
Slice the cucumbers into thin rounds or use a mandoline for even slices.
Julienne the carrots using a julienne peeler or grate them with a box grater.
Thinly slice the green onions, separating the white and green parts.
In a small bowl, whisk together soy sauce, rice vinegar, sesame oil, sugar, minced garlic, and grated ginger until the sugar dissolves.
In a large mixing bowl, combine the sliced cucumbers, julienned carrots, and green onions.
Pour the dressing over the vegetables and toss gently to coat everything evenly.
Sprinkle toasted sesame seeds over the top and give one final gentle toss.
Serve immediately or chill in the refrigerator for up to 30 minutes before serving for enhanced flavor.