Line a strainer with cheesecloth and place it over a mixing bowl large enough to fit the strainer. Spoon all of the yogurt into the strainer and refrigerate for 5-6 hours only. Then, pour off the liquid in the bowl and refrigerate the labneh in a tightly covered container for up to four days before serving. To serve the lebheh, spoon it into a bowl and give it a nice swirl on top with a spoon. Pour a tablespoon of olive oil into the swirl and serve, garnished with chopped dill.
Place the marinated chicken breasts on a sheet of aluminum foil on the hot grill and turn heat down to medium. Grill the chicken for 8 minutes and turn it over, removing it from the aluminum foil and placing the chicken directly on the grill. Next, grill the chicken for five minutes and turn it over, again placing it directly on the grill. Evenly divide the oil and parsley mixture over each chicken breast and grill for another five minutes. Turn the grill off and without opening the top, let the chicken rest for 10 minutes.
To serve the Mediterranean platter, artfully arrange the sliced chicken on the platter and place the eggplant, labneh and hummus (I love the recipe for Roasted Garlic Hummus from The Mediterranean Dish around the chicken. Fill in the spaces with Kalamata olives and feta cheese, garnishing the platter with chopped dill and lemon wedges, if desired.