Step 1Heat the broiler or prepare the grill with medium-hot coals.
Step 2Prick the eggplants deeply 5 or 6 times with a fork. Set the eggplants and chiles on a slotted broiler pan or in a roasting pan, lined with foil if you like, or on the grill. Broil or grill, turning the chiles often and turning the eggplants a few times, until the chiles are charred on all surfaces, about 7 to 12 minutes, and the eggplants are very tender, about 20 minutes. The eggplants should look collapsed, and their skins should be charred; check for tenderness by pressing on the neck end, or pierce it with a fork -- it should go in very easily.
Step 3Remove the chiles and eggplants from the oven or grill. If you have broiled the chiles on foil, enclose them in the foil; otherwise put the chiles in a bowl and cover, or put them in a plastic or paper bag and close the bag. Set aside until cool enough to handle, then peel with the aid of a paring knife. Cut the chiles in half, draining off any liquid. Discard the caps and remove the seeds. Cut the chiles into a small dice.
Step 4Cut off the eggplant caps. Halve the eggplants lengthwise. Scoop and scrape out the eggplant pulp from inside the skin. Put the eggplant in a colander and set aside for about 5 minutes to drain off liquid. Chop the eggplant pulp finely using a knife; you should have about 2 cups of pulp.
Step 5Transfer the eggplant to a medium bowl. Add the garlic and mix well.
Step 66. Spoon the tahini paste into a small bowl. Stir in the yogurt and mix gently. Stir in the lemon juice and mix until smooth.
Step 7Add the tahini mixture to the eggplant and mix well. Season with salt and freshly ground pepper to taste. If you like, stir in more tahini, yogurt or lemon juice.
Step 8Taste the diced chiles; the degree of heat in these chiles varies greatly. If they are mild, stir them into the eggplant mixture. If they are hot, add as much of them as you like. Taste and adjust seasoning. Refrigerate the dip for 1 to 2 hours to marry the flavors.
Step 9At serving time, spread the eggplant mixture in a thick layer on a platter or plate, making the edges slightly thicker than the center. Spoon part of the red pepper relish in the center and the rest into a small cup.
Step 10Drizzle the dip lightly with olive oil. Sprinkle the dip decoratively with parsley and Aleppo pepper.