In a mixing bowl, whisk together gochujang, gochugaru, soy sauce, sesame oil, rice vinegar, minced garlic, honey, and toasted sesame seeds until smooth and blended.

Bring a large pot of water to a rolling boil over high heat. Add the somyeon noodles and cook for 3-4 minutes, stirring occasionally to prevent sticking. Drain the noodles in a colander.

Immediately plunge the drained noodles into a bowl of ice-cold water for about 2-3 minutes. Drain them again and gently toss to remove excess water.

Place the cooled somyeon noodles in a large mixing bowl. Pour the prepared sauce over the noodles and gently toss to coat.

Transfer the coated noodles to a serving dish. Top with thinly sliced cucumber and a soft-boiled egg cut in half if desired. Serve with a side of kimchi.