Heat 1/4 cup oil in a large heavy skillet over medium heat. Add shallot and cook, stirring often, until translucent, about 2 minutes. Add the sliced garlic and cook until the edges just start to brown, about 2 minutes. Stir in tomatoes, 1 teaspoon salt and bay leaves. Cook, stirring often, until the tomatoes start breaking down and get super juicy, about 5 minutes.
Add eggplant and cook, stirring often, until it begins to soften, about 5 minutes. Stir in zucchini and cover pan. Reduce heat just a touch and cook until vegetables are tender, about 10-15 minutes (or more depending on the density of your vegetables). Season to taste with a bit more salt and stir in 1/4 cup parsley.
When ready to serve, add some freshly ground black pepper and garnish with remaining 1/4 cup parsley. Drizzle with olive oil.