01 - In a large bowl, combine beef broth, cold water, rice vinegar, sugar, soy sauce, sesame oil, and salt. Whisk thoroughly until sugar and salt completely dissolve. Refrigerate until ready to serve—the colder the broth, the better the final dish.
02 - Bring a pot of water to a boil. Cook eggs for exactly 10 minutes for hard-boiled consistency, then transfer to ice water to cool before peeling and halving. Meanwhile, thinly slice the cooked beef brisket, cucumber, Asian pear, and optional pickled radish. Keep all toppings chilled.
03 - Bring a large pot of water to a rolling boil. Add naengmyeon noodles and cook according to package directions, typically 3-4 minutes until al dente. Drain thoroughly and rinse under cold running water for 1-2 minutes, agitating gently to remove excess starch and stop the cooking process. Drain well.
04 - Divide the chilled noodles evenly among four serving bowls. Pour the refrigerated broth over the noodles. Arrange cucumber slices, Asian pear, beef brisket, and egg halves on top. Add 1-2 ice cubes to each bowl to maintain the coldest temperature.
05 - Sprinkle toasted sesame seeds over each bowl. Add a dollop of gochujang in the center if desired for extra heat and depth. Serve immediately with extra vinegar and mustard on the side for individual seasoning adjustment.