Place eggplant in a strainer and sprinkle with 1/8 teaspoon salt; let stand for 20 minutes and press out as much liquid as possible.
In a 4- to 5-quart slow cooker, combine eggplant, onion, bell peppers and mushrooms. Drain diced tomatoes and stir in along with tomato sauce, black pepper and Italian seasoning. Cook on HIGH for 3 hours or LOW for 5 hours.
Add squash into slow cooker for last 45 minutes of cooking time. Before serving, stir in basil and remaining 1/4 teaspoon salt and drizzle with olive oil, if desired.