Preheat the oven to 400 degrees . Prick the eggplants all over with a fork and place on a baking sheet. Bake, flipping once, until the skin is shriveled and the flesh softens, about 35 minutes. Let cool, about 30 minutes. Remove and discard the stems and skin. Cut the eggplant into large chunks and, using a colander, drain any excess liquid.
Using a food processor, puree the eggplant, parsley, lemon juice, tahini, garlic and 2 tablespoons olive oil. Season with salt and pepper, and add more lemon juice to taste.
Transfer the baba ghanoush to a bowl, drizzle with the remaining 1 tablespoon olive oil and serve with the pita wedges for dipping.