Step 1Heat the oven to 350 degrees. Cut the onion in quarters lengthwise and then in one-fourth-inch crosswise strips. Heat 3 tablespoons olive oil in a large skillet over medium heat, add the onion and cook, stirring occasionally, until it is softened and translucent, 6 to 8 minutes. Add the minced garlic and cook until fragrant, 2 to 3 minutes.
Step 2Generously oil an earthenware, glass or enameled cast-iron baking pan approximately 10 by 8 inches. Scatter the onions across the bottom, season lightly with salt and scatter the basil leaves over the top.
Step 3Arrange the zucchini on top of the onions in a single tight-fitting crosswise row. Arrange the remaining zucchini following the same pattern, overlapping each successive row by about one-half. Scatter the cherry tomatoes and black olives evenly over the top and again season lightly with salt (remember, the goat cheese will be slightly salty) and more generously with black pepper.
Step 4Crumble the goat cheese evenly over the top of the mixture, drizzle with olive oil and bake until the zucchini is very soft, the goat cheese is lightly browned, and most of the liquid from the vegetables has disappeared, 1 to 1 1/2 hours.