Put a large grill pan on two burners over medium-high heat or pre-heat an outdoor gas or charcoal grill to medium. If you’re using an outdoor grill, take a few paper towels and fold them over several times to make a thick square. Blot a small amount of oil on the paper towel, then carefully and quickly wipe the hot grates of the grill to make a non-stick surface.
Put the eggplant halves on a big platter or sheet pan. Drizzle with olive oil and sprinkle on both sides with salt and pepper. Put the eggplant slices on the grill and cook until golden, 4-5 minutes. Then turn and continue cooking 4-5 minutes more until nicely browned on both sides and soft and creamy.
Meanwhile, put the yogurt, tahini, lemon juice, 2 tablespoons olive oil, the cumin, and salt and pepper into a blender and puree until smooth. Taste for salt and pepper.
To serve, spread the yogurt sauce over the bottom of a serving platter. Shingle the eggplant halves on top and garnish with the mint, pomegranate seeds, and sliced chile.
Edited: November 4th, 2009