Smash the Cucumber: Place the cucumber on a flat, sturdy cutting board. Using the flat side of a heavy cleaver, a meat pounder, or the bottom of a heavy skillet, whack the cucumber firmly but gently along its entire length until it splits open and flattens.
Salt and Drain: Cut the smashed cucumber crosswise into 1-inch bite-sized pieces. Place them in a colander set over a bowl. Toss generously with kosher salt and let sit in the refrigerator for 10 minutes. This draws out excess water and concentrates the flavor.
Combine: Discard the liquid collected in the bowl. Transfer the drained cucumbers into the bowl and add the minced garlic, vinegar, and sesame oil. Toss thoroughly to coat.
Garnish and Serve: Top the salad with the sliced fresh chili and a generous handful of chopped parsley. Serve immediately, as the salad will lose its crunch if left to sit for too long.