Put an oven rack in the center of the oven. Preheat the oven to 375 degrees F. Butter a 13 by 9-inch baking dish. Place a grill pan over medium-high heat or preheat a gas or charcoal grill.
Drizzle the eggplant, fennel and zucchini slices with olive oil. Season with salt and pepper. Grill the vegetables until softened, 3 to 4 minutes each side. (The vegetables can also be baked in a 375 degrees F oven for 15 to 20 minutes until soft).
Spoon 3/4 cup of the marinara sauce over the bottom of the prepared baking dish. Arrange the eggplant slices on top. Sprinkle with 1 cup of mozzarella cheese and 1/3 cup Parmesan cheese. Arrange the fennel slices in a single layer on top. Spoon 3/4 cup of marinara sauce over the peppers. Sprinkle with 1 cup of mozzarella cheese and 1/3 cup Parmesan. Arrange the zucchini on top and cover with the remaining sauce. Sprinkle with the remaining cheese. Scatter the bread crumbs over the cheese and drizzle liberally with oil. Bake until the top is golden and forms a crust, 30 to 35 minutes.