Grate the cucumber on the large holes of a box grater. Wrap the shreds in a clean kitchen towel and squeeze firmly until you have about ½ cup of dry cucumber.

In a bowl, whisk the yogurt, garlic, lemon juice, dill, mint (if using), salt, and pepper until smooth.

Fold in the cucumber, then cover and refrigerate for at least 15 minutes. Serve in a bowl drizzled with olive oil and topped with sumac or dill.