Slice Cucumber lengthwise and scoop out seeds with a spoon. If using an English Cucumber you can skip de-seeding. Place in colander and sprinkle with kosher salt to remove excess water. Leave in sink for 30 minutes then rinse off salt and pat dry with a towel.
While your cucumber is sitting, cube Avocado. I do this by slicing the avocado in half lengthwise and removing the pit. Then take a paring knife and slice about five slices up and down while still in its skin. Then scoop out with a spoon. Immediately squeeze half of the lime over the avocado to keep it from browning.
Squeeze remaining 1/2 of lime into a small bowl, add the EVOO and salt and pepper and whisk.
Add cucumber, finely chopped de-seeded Jalapeno, Cilantro and olive oil and lime mixture to the avocado. Mix gently so not as to smash all the avocado too much. Taste and add more salt, pepper or lime if you like.
Chill for at least 1/2 an hour to let the flavors meld and server.