Heat a stockpot of salted water to a boil. Cook pasta according to package directions.
Meanwhile, heat oven to 400 degrees. Line 1 large baking sheet with foil; brush a generous amount of olive oil over surface. (This will coat base of vegetables and also make them easy to remove.) Add eggplant and onion to cover about two-thirds of pan; it's OK if they're squished together; the vegetables will shrink while roasting. Drizzle additional olive oil over vegetables, then use a silicone brush to distribute over them.
Put tomatoes in large serving bowl; add about 2 teaspoons olive oil. Stir to coat.
Sprinkle 1 1/2 tablespoons Italian seasoning over vegetables on pan, and 1 teaspoon over the tomatoes. Sprinkle salt and pepper to taste on both vegetables and tomatoes. Bake eggplant and onions, 10 minutes.
Remove pan from oven; stir ingredients and break up the onions a bit. Add cherry tomatoes to pan. Use brush to move tomatoes around to distribute oil and seasoning. Drizzle balsamic vinegar over all ingredients; use brush to distribute. Bake until fork pierces easily through the onion and eggplant, 10 to 15 minutes.
Drain pasta; pour into large serving bowl. Stir in butter until it's melted. Add roasted ingredients, including juices; stir. Scatter basil over top. Add cheese or pass for serving.