Grate the cucumber with a box grater or finely chop it in a small food processor, then toss it with 1/2 tsp of the kosher salt. The salt starts drawing out moisture right away, and the cucumber should begin looking glossy and wet.

Transfer the salted cucumber to cheesecloth or a double-thick napkin and squeeze out as much liquid as possible. You’ll be surprised by how much comes out, and the cucumber should feel damp and clumpy, not wet.

In a large mixing bowl, combine the garlic, the remaining 1/2 tsp kosher salt, the white vinegar, and the olive oil. The mixture should smell sharp and lively, with the salt helping the garlic break down into the liquid.

Add the drained cucumber, then stir in the Greek yogurt, white pepper, and the chopped dill or mint if using. Mix until the sauce looks evenly creamy with no watery pockets around the edges.

Cover and refrigerate for at least 30 minutes and up to a couple of hours before serving. This resting time thickens the texture and rounds out the garlic so the flavor tastes more blended and balanced.

Stir the tzatziki again just before serving, then spoon it into a bowl and drizzle with a little more olive oil if you like. The finished sauce should look thick, cool, and creamy enough to mound lightly on a spoon.