Slice and Salt the Cucumbers — Trim the ends and slice into thin rounds, about 1/8 inch thick. Place in a colander over a bowl, sprinkle with salt, toss gently, and let sit 10 to 15 minutes.
Drain and Pat Dry — Press the cucumbers gently to squeeze out liquid, then pat dry with paper towels. Don't rinse.
Mix the Dressing — Whisk together the soy sauce, rice vinegar, gochugaru, sugar, garlic, and sesame oil until the sugar dissolves.
Toss the Cucumbers in the Dressing — Add the drained cucumbers to a large bowl, pour the dressing over, and toss gently until coated.
Finish and Serve — Sprinkle with sesame seeds and green onions, toss lightly, and chill 10 to 15 minutes before serving. Add red onion just before serving.