Cut tomatoes into 1⁄4-inch-thick slices. Place slices in a colander over a bowl. Salt, to taste, and toss to coat. Set aside to drain for 30 minutes.
Rinse and dry zucchini. Slice each one into 1⁄4-inch-thick slices, cutting slightly on the diagonal. Put slices into a bowl, salt, to taste, and toss lightly. Set aside for 15 to 20 minutes.
Preheat oven to 400°F. Butter a shallow, 13x9-inch baking dish or large gratin dish. (For a slightly richer version, if using the heavy cream, pour it into the dish and tilt to coat.)
Combine bread, Parmesan, and parsley in a food processor. Pulse to reduce bread to fine crumbs. Transfer to a bowl and add basil, ¼ teaspoon salt, and pepper. Mix to blend.
Lay zucchini slices on paper towels and pat dry. Lay tomato slices in the bottom of the prepared baking dish. Place zucchini slices on top. Spread bread crumbs over zucchini and evenly drizzle oil on top. Bake for about 30 minutes, or until bubbly.