Peel, deseed, and dice the cucumber. Typically Malabar cucumber's are used to make this curry but I've made it with other types of cucumbers too and they work just fine.
Add diced cucumber, slit green chili and salt along with around 1/4 cups of water and cook on low.
While the cucumber is cooking, add all the coconut mixture ingredients to a blender.
This is the kind of silken tofu I usually use. Since it's shelf-stable it's convenient to keep a few in the pantry.
Blend to a smooth paste.
Add the coconut paste to the cooked cucumber and mix well.
Cook for another minute or two.
Meanwhile, heat coconut oil in a pan, when it's hot add mustard seeds, whole red chili, and curry leaves. When you put the curry leaves in be prepared for a lot of spluttering. You can put a lid on right afterward for a few seconds to prevent all the mustard seeds from popping out and to protect yourself from splattering oil.
Mix in the tempered oil into the cucumber mixture and enjoy!