SCRAPE the seeds out of the cucumber halves using the pointy end of a teaspoon, and discard. GRATE the cucumber flesh into a bowl then squeeze out any excess moisture using your hands (a small handful at a time works best). PLACE the grated cucumber into a large bowl and add the yogurt, garlic, lemon juice, olive oil, dill, and salt. STIR well to combine. PLACE the tzatziki in the refrigerator for at least 2 hours (and preferably overnight) to let the flavors meld and intensify.

Variation: Use finely chopped fresh mint instead of dill.