Heat 3 tablespoons of the olive oil in a large skillet over medium heat. Add the eggplant along with a small pinch of salt and sauté until tender, about 8-10 minutes. Transfer to a bowl.
Pour another tablespoon of olive oil into the skillet. Add the zucchini and yellow squash. Season with a small pinch of salt and saute until tender, about 5 minutes. Transfer to the bowl with the eggplant.
Pour in the remaining tablespoon of olive oil. Add the onion and red pepper and saute until tender, about 5-6 minutes.
Add the garlic and cook until fragrant, about 30 seconds.
Add the tomatoes, thyme, and a large pinch of salt to the skillet. Cook the tomatoes down until they are extremely tender and their juices have released, about 8-10 minutes.
Add the eggplant and squash back to the skillet. Simmer for another 4-5 minutes.
Stir in the basil and season with black pepper and more salt to taste before serving.
