The night before: Strain yogurt in cheesecloth over a bowl in the refrigerator. This removes excess whey and creates the thickest, creamiest base.
Grate cucumber on the large holes of a box grater. Wring in a kitchen towel — squeeze hard, release, squeeze again. All the water must come out.
Work minced garlic with salt on a cutting board until it becomes a smooth paste (or use a mortar). This removes harshness.
Combine strained yogurt, squeezed cucumber, garlic paste, dill, mint, olive oil, and vinegar.
Mix well. Taste and adjust — it should be cool, tangy, garlicky, and herbaceous.
Refrigerate at least 2 hours before serving. Always serve cold with a fresh drizzle of olive oil.