Be sure BBQ grates are clean. Preheat BBQ to 500°F or higher.
Cut 4 strips of parchment paper, 6” X 12”, one for each pizza. Lightly grease.
Divide dough into 4 portions and place each portion on parchment strips. Use fingers to create an oblong shape, about ¼” thick. Brush with olive oil.
To grill, use parchment paper as a guide to flip dough directly on grill, paper side up. Peel off the parchment paper. Work quickly to lay a few doughs on the grill and close the lid to retain the heat. (To work quickly, you can leave paper on, close lid to bring temperature up, and then remove paper.)
After a few minutes, use tongs to flip the pizza to grill the other side. The dough is ready when it has risen, turned golden with charred grill marks.
If using immediately, reduce the heat. While still on the grill, dress with sauce, cheese, and toppings. Close lid for a minute or two to heat up toppings.
Carefully remove and slice.
Serve with an extra drizzle of olive oil.