Bring a pot of water to a boil. Add the naengmyeon noodles and cook for a few minutes according to package instructions until chewy but tender.
Drain the noodles and immediately rinse them under cold water until completely chilled. This step is key for that signature chewy texture.
While the noodles cook, prepare the sauce. In a bowl, mix together gochujang, gochugaru, brown sugar, vinegar, soy sauce, sesame oil, garlic, cold water, and sesame seeds. Stir until smooth and glossy. Set aside.
Place the chilled noodles in a bowl or plate, neatly arranged.
Add the sauce on top of the noodles.
Arrange the julienned cucumber over the sauce and place the boiled egg halves on top or to the side.
Add a few ice cubes to the bowl to keep everything extra cold.
Pour a small amount of the cold naengmyeon broth into the bowl, just around the bottom (not too much).
Finish with an extra sprinkle of sesame seeds.
Mix everything together before eating and enjoy immediately.