Preheat the oven to 375 degrees F.
Place the one-third of the zucchini slices inside a baking dish. Scatter one-third of the onions over top. Dollop one-third of the Pistachio Pesto on top of the onions. Layer one-third of the tomato slices over top and season well with salt and pepper. To begin the second layer, place another third of the zucchini in the opposite direction and repeat the process with the addition of dollops of 1/4 cup of the goat cheese. Repeat the process for one more layer, then place the remaining goat cheese on top. Sprinkle with the breadcrumbs and garnish with the pistachios. Bake until the zucchini is tender and the breadcrumbs are golden, 20 to 30 minutes. Allow to rest and set before slicing.
In batches, place the basil leaves, oil, pistachios, Parmesan and garlic in a blender and puree until smooth. Season with salt and pepper. Place the Pistachio Pesto in a container. Cover the top with the remaining 1 tablespoon olive oil.