Prep the vegetables: Julienne the cucumber and carrot. Shred the cabbage or lettuce. Slice radishes thin.
Set everything in the fridge to keep it crisp.
Make the sauce: In a bowl, whisk gochujang, soy sauce, rice vinegar, sugar or honey, sesame oil, garlic, and optional gochugaru and ginger. Add cold water, 1 tablespoon at a time, until pourable but still thick.
Cook the noodles: Bring a large pot of salted water to a rolling boil. Add somyeon and cook 3–4 minutes or until just tender.
Rinse and chill: Drain and immediately rinse noodles under very cold water.
Rub gently with your hands to remove starch. Drain well.
Toss with sauce: In a large bowl, combine cold noodles with the sauce until evenly coated.
Assemble: Top with cucumber, carrot, cabbage or lettuce, and radishes. Add egg, tuna, kimchi, or pear if using.
Garnish and serve: Sprinkle sesame seeds, scallions, and seaweed strips.
Taste and adjust with more vinegar for tang, sugar for sweetness, or gochugaru for heat.