Preheat oven to 400°F. Place a sheet of parchment paper on a rimmed baking sheet. Place puff pastry on parchment, and roll pastry into a 14- x 11-inch rectangle. Fold pastry edges to create a 3/4-inch border; prick pastry beside border evenly with a fork. Place a sheet of parchment over the pastry, and place pie weights evenly over pastry inside border. Bake pastry in preheated oven until golden brown, about 30 minutes. Remove pie weights, and discard top sheet of parchment.
Toss shaved zucchini with 2 tablespoons of the Summer Sauce. Top pastry evenly with zucchini, Parmesan, and remaining 1 tablespoon Summer Sauce. Sprinkle tart with kosher salt and black pepper.
Cut tart into 12 pieces and serve.