Place the yogurt in the center of the double layered cheesecloth. Standing over the sink, twist the muslin around the yogurt until you have a tight ball. Tie the top with some string and suspend the ball (I tie it to the tap) overnight. You will end up with a yogurt of a very thick consistency, which is known throughout the Eastern Mediterranean as suzme. You will have about 1 1/2 cups. Cover and refrigerate.
Combine the beets, garlic, lemon juice and suzme, and season.
Serve drizzled with the olive oil, andsprinkled with the parsley and walnuts.