Peel the cucumber into long strips such that you're alternating one long peeled length with one long unpeeled length. When you're done, you should have a cucumber zebra, so to speak :D You're doing this to add a little color variation, and also to allow the sauce to flavor but not water-log the outside of the cucumber. This is a tiny affectation that you could skip entirely.
Cut the cucumber into fourths lengthwise and then cut into chunks.
Using the flat of your knife--or a cleaver if you trust yourself with one, I can't be trusted with one--roughly smash the cucumber on the side to smoosh it a bit. You want it to crack but not turn into cucumber purée.
In a bowl mix all the sauce ingredients. Taste and adjust as needed.
15-20 minutes prior to serving, pour the sauce over the cucumbers.
Add cilantro and crushed peanuts (which just totally complete this dish!) and mix well before serving.
Substitutions:
Use crushed Sichuan Peppercorns or red pepper flakes instead of the chili crisp oil, although that oil! Oh my!
If you don't have Chinkiang Vinegar, use the mildest, least tart vinegar you have and give it a shot.
If you have a peanut allergy, I'd try toasted pecans or skip entirely