Prick eggplant with a fork several times and on a baking sheet rub with just enough oil to coat.
Cut off and discard top quarter of garlic head to expose cloves and set garlic in middle of a large piece of foil. Drizzle garlic with 1 teaspoon oil and enclose completely in foil. Place foil packet next to eggplant on baking sheet and roast in middle of oven, turning eggplant after 30 minutes, 45 to 50 minutes, or until eggplant is very soft and collapsed. Unwrap garlic carefully and cool eggplant and garlic on baking sheet.
Transfer eggplant to cutting board. Cut off and discard stem end and halve eggplant lengthwise. Scoop flesh out into a bowl, scraping as close to skin as possible. Pour off any liquid accumulated in bowl.
Squeeze roasted garlic from skins into a food processor. Add eggplant, lemon juice, tahini, parsley, and salt to taste and blend until smooth and parsley is minced fine. Dip may be made 1 day ahead and chilled, covered.
Transfer dip to a bowl and serve with pita wedges.