In a large saucepan, heat 2 tablespoons olive oil over medium heat. Add the onion and garlic and cook, stirring occasionally, until soft, about 5 minutes. Stir in the eggplant, zucchini and 1 cup water, season with salt and pepper and cook, stirring frequently, for 5 minutes. Add the tomatoes and their juice and bring to a boil. Lower the heat, partially cover and simmer, stirring often, until the vegetables are tender, about 15 minutes. Stir in the basil.
Meanwhile, preheat the oven to 400 degrees . Brush both sides of each baguette slice with the remaining 2 tablespoons olive oil and arrange on a baking sheet; season with salt. Bake until browned, about 12 minutes.
Spread the goat cheese on the toasts. Preheat the broiler, then broil the toasts until the cheese is hot, about 1 minute. Serve with the stew.