Preheat oven to 375°F. Generously oil rimmed baking sheet. Place eggplant halves, cut side down, on sheet. Roast until eggplant is very soft, about 45 minutes. Cool slightly. Using spoon, scoop out pulp from eggplant into strainer set over bowl. Let stand 30 minutes, allowing excess liquid to drain from eggplant.

Transfer eggplant pulp to processor. Add 1/4 cup oil, tahini, lemon juice, and garlic; process until almost smooth. Season to taste with salt and pepper. Transfer to small bowl. (Can be made 1 day ahead. Cover and chill. Bring to room temperature before serving.) Serve with pita wedges.