In a large bowl, toss together the tomatoes, cucumber, and salt. Let sit until juicy, about 10 minutes.
Add the vinegar, soy sauce, sugar, garlic, mustard and sesame oil to the tomatoes and cucumber, and toss with a spoon until well combined. Stir the filtered water into the tomatoes and cucumber and sprinkle the surface of the broth with the sesame seeds, cucumber, and scallions.
Right before serving, add the ice to the broth. Divide the noodles among bowls, and ladle in the broth and any unmelted ice, making sure each serving gets a nice sprinkling of tomatoes, cucumbers, scallions and sesame seeds. Garnish each bowl with cilantro and halved boiled egg (if desired).