Slice the cucumbers. Sprinkle with 1/2 teaspoon of salt (optional). Set aside.
Boil water, and pour 1/2 cup into a bowl, add the sugar, and whisk until dissolved. Add remaining broth ingredients in large bowl and combine.
Rinse cucumbers, then add to broth to marinate.
Cook the noodles according to package direction. This usually takes about 5-7 minutes.
Drain noodles and rinse well.
Add the noodles to the broth, add additional seasoned vinegar if desired, and chill for 30 minutes to 1 hour.
Make and add additional broth if desired. The kind of noodles you use and length of chilling can impact how much broth you will need (if a small amount is needed, I'll often just add a bit of water).
Notes
Note that this is a large serving of this dish. For a side dish, this should make about 8 servings.