Sicilian Style Spaghetti and Eggplant

Name: Sicilian Style Spaghetti and Eggplant
Ingredients: 2 medium eggplants; 1/4 cup plus 2 tablespoons extra-virgin olive oil; 2 garlic cloves; 1/2 lemon, juiced; 6 fresh basil leaves; Kosher salt and freshly ground black pepper; 3 tablespoons extra-virgin olive oil; 2 medium onions, chopped; 1 fresh red chile, chopped; 2 garlic cloves, minced; 1 cup alfonso olives, pitted; 1/2 bunch fresh basil leaves; 3 (28-ounce) cans whole peeled tomatoes, drained and hand-crushed; Pinch sugar; 1 tablespoon capers; 1 pound spaghetti; 1/2 cup freshly grated pecorino cheese