Season eggplant with salt; place in a colander with a weight on top to drain for 2 hours.
Bring a large pot of water to a boil. Cook pasta according to package directions.
Meanwhile, in a skillet sauté onion with olive oil for three minutes, add sweet potato and eggplant. Continue cooking for 3-4 minutes, then add broth, bring to boil and simmer until both potato and eggplant are cooked through, season with salt and pepper.
Drain pasta, toss with veggies, stir in basil leaves and cheese.
