Wash the cucumber thoroughly and slice it thinly into 1/8-inch rounds. Place the sliced cucumber in a bowl and toss with the coarse sea salt, mixing well to coat all pieces evenly. Let this sit for 15 minutes—the salt will draw out excess water from the cucumber, which concentrates its flavor and prevents the salad from becoming watery. This is a crucial step for achieving the right texture.

While the cucumber sits, whisk together the gochugaru, rice vinegar, sugar, freshly minced garlic, gochujang, toasted sesame oil, and soy sauce in a small bowl. Stir until the sugar dissolves completely and the sauce is well combined and uniform in color. I like to taste a tiny bit at this point to adjust the balance—if it's too spicy, add a touch more rice vinegar or sesame oil to balance the heat.

After 15 minutes, drain the cucumber in a colander and gently squeeze it with paper towels to remove excess moisture—but don't compress it too much or the slices will break apart. Transfer the dried cucumber to a fresh bowl, then add the thinly sliced onion and toss gently to combine. The onion will soften slightly from any remaining moisture on the cucumber, which is exactly what you want.

Pour the seasoning sauce from Step 2 over the cucumber and onion mixture and toss gently but thoroughly to coat everything evenly. Sprinkle the sesame seeds on top and give it one final gentle toss. Refrigerate for at least 30 minutes before serving—I find that this resting time allows the flavors to meld beautifully and the cucumber to reach the perfect texture, not too crisp and not too soft.