Using tongs, cook eggplants one at a time over the flame of a gas burner (or a grill), turning as skin chars and bubbles, until completely soft, about 15 minutes. (If eggplant doesn't soften, finish cooking on a baking sheet in a 375-degree oven.) Let stand until cool enough to handle, about 15 minutes. Peel off charred skin and discard. Coarsely chop the eggplants, and place in a colander to drain, about 1 hour. Finely chop, and transfer to a bowl.
Using a chef's knife, press flat side of blade back and forth across garlic and 1 1/2 teaspoons salt to make a paste. Mix into eggplant. Stir in oil. Mix in yogurt and lemon juice, and season with salt and pepper. (Dip can be refrigerated, for up to 1 day.) Drizzle with oil before serving.
On "Mad Hungry," Lucinda served this dip with homemade flatbread and veggies.