Preheat grill over medium-high heat.
Oil barbeque grill topper or a baking sheet tray. With your hands work the dough ball out onto a lightly floured surface into a rectangular shape about 1-inch thick. Shape doesn't have to be perfect. Place dough on lined baking sheet. Brush with some olive oil, then sprinkle top with grated Parmesan. Place 1 row of zucchini rounds along 1 side of dough. Working in and along side of the zucchini arrange 1 row of shallots followed by another row zucchini. With your fingertips gently press vegetables into the dough. Drizzle with 1 tablespoon olive oil. Place on preheated grill and cook for about 20 to 25 minutes until golden brown and crispy. Remove from grill, cut and serve warm.