Cook somen according to package directions until tender.
Drain and rinse thoroughly under iced water, rubbing gently to remove excess starch.
Drain very well.
Make the Sauce
In a large bowl, whisk together Korean chili paste, sugar, rice vinegar, kimchi juice, soy sauce, sesame oil, Korean chili flakes, and chopped kimchi until smooth.
Add the drained noodles to the bowl and toss until thoroughly mixed.
Assemble
Divide noodles into bowls.
Top with halved hard-boiled eggs, julienned cucumber, and pear or apple if using.
Finish with toasted sesame seeds or crushed seaweed.
Serve
Serve immediately while the noodles are cold and springy.
Notes
Rinse noodles thoroughly to remove starch and keep them springy. Balance sweetness and acidity by adjusting sugar and kimchi juice to taste. Best served immediately while chilled.