Cook until grill marks begin to form and dough begins to puff slightly, 1 to 2 minutes. Using tongs, peel dough carefully from grates and rotate 30 degrees or so. Bake until underside is lightly and evenly browned, 2 to 3 minutes more. Transfer to a second baking sheet. Repeat steps 9 and 10 with remaining dough balls, adding oil to baking sheet only if necessary.
If you have a large grill surface, you may be able to cook two crusts at a time.