Slice the cucumber thinly.
Sprinkle salt over the cucumber and let it sit for a while.
In a bowl, combine water, vinegar, sugar, salt, and ice. Mix well.
Squeeze out excess moisture from the cucumber and add it to the soup base.
Add minced garlic, sesame seeds, and julienned chili pepper, then mix.
Serve in a bowl and chill in the refrigerator before serving.