In Greece, this dish is called melitzanosalata. The eggplants can be grilled instead of broiled.
Heat broiler. Prick eggplants several times with the tip of a knife. Broil 3 to 4 inches from heat, turning occasionally, until soft and charred all over, about 30 minutes. When cool enough to handle, remove skin. Place eggplants in a colander set over a bowl; let drain for at least 30 minutes.
Halve eggplants lengthwise; discard seeds. Chop flesh finely, and place in a bowl.
Combine vinegar, lemon juice, olive and vegetable oils, onion, garlic, sugar, salt, and pepper. Add to eggplant; mix to combine. Serve at room temperature sprinkled with chopped mint and parsley.