Add the cubed eggplant to a colander. Place the colander in the sink, sprinkle with ½ teaspoon salt, and toss to combine. Set aside for 30 minutes while you cook the onions and chop the remaining vegetables.
Heat a large skillet over medium heat. Add 2 tablespoons of olive oil and the red onion. Sprinkle with a pinch of salt, and cook until softened, about 5 minutes, stirring occasionally. Add the tomato paste and garlic, and cook until fragrant, about 1 minute, stirring constantly. Add the wine, stirring to scrape any browned bits from the bottom of the pan.
Carefully transfer the onion-tomato paste mixture to a 6-quart slow cooker. Give the eggplant a very gentle squeeze to remove any excess liquid, then add it along with the bell pepper, zucchini, yellow squash, tomatoes, Italian seasoning, and pepper.
Add the remaining 1 tablespoon olive oil and 1 teaspoon salt. Stir until well combined.
Cover and cook on high for 3-5 hours, or low for 5-7 hours.
Uncover and add ½ teaspoon salt. Taste and adjust seasoning if desired.
To serve, remove from the slow cooker and allow to cool to room temperature or refrigerate. Sprinkle with fresh basil and serve as desired.
