Grate the cucumber using a box grater or finely chop it in a small food processor.
Toss the grated cucumber with half of the kosher salt and place it into a cheesecloth or double napkin to squeeze out excess liquid.
In a large bowl, combine the garlic, remaining salt, white vinegar, and olive oil, mixing well.
Add the drained cucumber to the bowl along with the Greek yogurt, a pinch of ground white pepper, and fresh herbs if using; mix everything thoroughly.
Cover the bowl and place it in the refrigerator for at least 30 minutes up to 2 hours to thicken the sauce and develop flavors.
Before serving, stir the sauce gently to refresh it, transfer to a serving dish, and optionally drizzle a bit more olive oil on top.
Serve chilled with warm pita bread or sliced vegetables for dipping.