Grill the eggplant over the gas grill or prick and roast in a hot oven until it is extremely soft inside.
When cool, split the eggplant open and gently scrape the seeds out, using a melon-baller or large spoon. Pull away the skin, drain the liquid, and chop the pulp in 1/2-inch cubes.
Gently score the outer skin of the pomegranate into quarters. Place the entire pomegranate in a large bowl filled with water. With your hands under the water, gently pull the skin off and remove the seeds, which will fall to the bottom. Drain off the water, discard the outer skin and fiber, dab the seeds dry, and proceed. Reserve 1/4 cup of the seeds for garnish.
Place the remaining seeds over a sieve and press out the juice with your hands. You should have approximately 1/4 cup juice. Discard the pulp and seeds.
In a nonmetallic bowl, mix the eggplant with the pomegranate juice, tahina, lemon juice, salt and garlic. Adjust the amount of pomegranate juice and lemon to your taste. In a food processor fitted with a steel blade, pulse the mixture until smooth but not mushy.
Spread mixture on a flat suraface and sprinkle with chopped parsley and the reserved pomegranate seeds, dried cherries, or dried cranberries. Serve with pieces of warm pita for dipping.