In a small sieve lined with a dampened paper towel and set over a bowl, drain the yogurt in the refrigerator until it is thick and has the consistency of soft cheese, about three hours.
To make the dressing, combine the oil, vinegar, mint, and salt and pepper in a small container with a tight-fitting lid. Refrigerate.
In a large container with a tight fitting lid, place radishes, tomatoes, and cucumber; over vegetables with waxed paper, and then place lettuce on top of them. Cover the container and refrigerate.
To serve, remove waxed paper, shake dressing to combine, and pour over salad. Add crumbled yogurt cheese; toss to combine. Serve with pita bread, if desired.
If you can't find Greek yogurt, substitute another yogurt. Or use a storebought yogurt cheese, feta, or a soft goat cheese. Keep the salad and dressing separate, and toss before serving.