Preheat oven to 400°F with rack in middle.
Cut off and discard top of garlic head to expose cloves. Brush top of head with 1/2 tablespoon olive oil. Wrap garlic in foil and roast until tender, about 45 minutes. Cool to warm, then squeeze garlic cloves from skins into a small bowl, discarding skins.
Meanwhile, cut eggplant into 1/2-inch pieces and toss with 1 1/2 teaspoons salt in a large colander. Let drain 30 minutes. Squeeze eggplant in a kitchen towel to remove liquid.
Heat 2 tablespoons olive oil in a 12-inch heavy skillet over medium-high heat until it shimmers, then sauté one third of eggplant until browned and tender, about 6 minutes. Transfer to a bowl. Cook remaining eggplant in olive oil in same manner (in 2 batches), transferring to bowl.
Add 1 cup cooked eggplant to garlic and coarsely mash together. Stir into remaining eggplant with sun-dried tomatoes (without tomato oil), parsley, basil, lemon juice, and 3/4 teaspoon pepper. Season with salt and drizzle with tomato oil.