Place each eggplant directly over a gas flame on the stove, or place all three on a rack over a hot barbecue (the coals should be white). Cook, turning it often, until blackened, blistered, and charred. Each eggplant will take about 15 minutes. This is a smoky process, so open a window or use an extractor fan. Alternatively, heat the broiler to its highest setting, place the eggplants underneath, and cook until charred all over and completely collapsed. 

Transfer the cooked eggplants to a strainer set over a bowl or the sink and let drain and cool. When cool enough to handle, place on a board and slice open lengthwise, so they open like a book. Scoop out the soft flesh with a spoon, discarding any seedy pieces. 

Put the flesh into a bowl with 2 tablespoons of the lemon juice and the garlic and mash coarsely. Next add the tahini, if using, and olive oil, then mix and mash until you have a textured, creamy puree. Stir in the chopped parsley. Taste and add the rest of the lemon juice and the salt, if needed. The finished dip should be smoky, sharp from the lemon, and garlicky. 

The dip will keep, covered, in the refrigerator for a couple of days, but is best served at room temperature.