Preheat oven to broil. Prick eggplants all over with fork. Place on shallow baking pan. (For easier clean-up, line pan with foil.) Broil about 12 minutes or until skin is charred on all sides, turning occasionally. Reduce oven temperature to 400°F. Bake 15 to 20 minutes longer or until eggplant flesh is tender. Let stand until cool enough to handle.
Cut eggplants in half lengthwise. Scoop flesh into colander, discarding charred skin and as many of the seeds as possible. Drain 30 minutes, stirring occasionally. Place eggplant, tahini, lemon juice, all purpose seasoning, cumin and smoked paprika in food processor; cover. Process until smooth. If needed, add 1 to 2 tablespoons of the olive oil for smooth texture. Season to taste with salt and pepper.
Spoon dip into serving bowl. Drizzle with remaining 1 tablespoon olive oil. Sprinkle with parsley. Serve with pita wedges, French bread slices or crackers.