Place a large pot of water over high heat to cook the pasta. When the water is boiling, add some salt and drop the pasta. Cook to al dente according to package directions. Just before draining, reserve a mug of starchy cooking water (about 1/2 cup). Drain the pasta and reserve.
Place a large skillet over medium-high heat with 3 turns of the pan of EVOO, about 3 tablespoons. Add the eggplant, onion and garlic to the pan. Give everything a toss to coat with oil then cover the pan. Cook the veggies, stirring occasionally, until tender, 5-6 minutes.