For the crust: Preheat the oven to 350 degrees F.
Combine cornmeal, pastry flour, and salt in the bowl of a food processor. Pulse to incorporate. Add butter and oil and pulse about 20 times, until mixture resembles small pebbles. Add water and pulse until mixture forms a loose dough. Remove dough from processor and press into bottom and about 1/8-inch up the sides of a 9-inch tart pan with a detachable rim. Press aluminum foil into the bottom and sides of the pan on top of the dough and weigh down with uncooked rice or pie weights. Place tart pan on a baking sheet and bake for 10 minutes. Remove from oven and remove rice and foil. Return to oven and bake for an additional 5 minutes, or until no longer shiny and wet. Remove from oven and let cool.
For the filling: Increase the oven to 400 degrees F. Heat 1 teaspoon of olive oil in a nonstick pan over medium heat; saute shallots until soft, about 5 to 6 minutes. Spray 2 baking trays with cooking spray. Arrange the eggplant, zucchini and tomato slices on the trays in a single layer and brush with the remaining olive oil. Season with salt and pepper, and roast the vegetables until soft but not browned, about 15 minutes. Remove the vegetables from oven and cool.
Lower the oven temperature to 350 degrees F. Lay the eggplant slices in 2 layers on the bottom of tart; cover with 1/3 of the mozzarella cheese and some of the shredded basil. Add the zucchini and shallots, top with another 1/3 of the mozzarella and basil, then the tomatoes. Top with rest of the mozzarella cheese and the Parmesan. Bake for 25 to 30 minutes, or until cheese is melted and vegetables have further wilted. Remove from oven, let cool for 5 minutes, and cut into 8 slices. Serve warm.