Set a strainer over a bowl and line it with paper towel or cheesecloth. Add 2 cups Greek yogurt.
Cover and refrigerate at least 10 hours/overnight to drain.
The next day, discard the liquid; the yoghurt will be very thick (like labne cheese).
Prepare 1 cucumber: peel, halve, deseed, coarsely grate, finely chop, then squeeze extremely well (over the sink) to remove as much liquid as possible. Stir into the thick yogurt.
Add garlic, lemon juice, olive oil, and salt to taste. Mix well.
Optional: fold in ~1 Tbsp dill (or mint). Taste; you added a second cucumber for extra texture/looks, so do the same if you like.
Spoon into a serving bowl; garnish with dill or mint (if used) and a little lemon zest.
Storage: Keeps refrigerated for up to 2 weeks, or as long as the yogurt’s use-by date.