Preheat oven to 350°F. Cut eggplant in half lengthwise, then score flesh in crisscross pattern at 1-inch intervals, 1/2 inch deep. Rub cut sides with 1 1/2 tablespoons oil; sprinkle with salt. Place eggplant on rimmed baking sheet, cut side down; bake until tender, about 1 1/2 hours. Cool slightly, then scoop flesh into processor (discard skins). Add garbanzo beans, remaining 1 1/2 tablespoons oil, lemon juice, tahini, and garlic; puree until mixture is almost smooth. Transfer to bowl; stir in parsley. Season hummus to taste with salt and pepper.