Preheat a broiler or prepare a medium-hot charcoal fire. Bring a large pot of salted water to a boil.
Cut eggplant in half lengthwise and place cut side down on a broiling pan or cut side up on oiled grates. Broil or grill until skin is crinkly and hard, about 15 minutes. Transfer to a large bowl and cover with plastic wrap. Set aside to steam for 10 to 15 minutes. Transfer to a work surface and carefully scrape out flesh, discarding skin. (Eggplant will be hot, so use a kitchen towel to hold one end while you scrape out flesh with a large spoon.)
Add zucchini and yellow squash to boiling water and bring back to a boil. Cook for 1 minute or until just tender. Use a slotted spoon to remove, transfer to a colander and run under cold water. Drain on paper towels and pat dry. Keep water at a full boil.
Add pasta to boiling water and cook until al dente, 10 to 12 minutes, depending on package directions. Drain and run under cold water. Shake colander to remove as much water as possible, and place pasta in a large bowl. Add oil, vinegar, eggplant, zucchini and squash. Stir in basil; toss well and season generously with salt and pepper. Serve at room temperature.