Preheat the grill, setting one burner on medium-high and the other on medium-low. The actual temperature setting will depend on your grill and how hot it cooks. The hotter side should cook one side of the crust quickly, in just a few minutes.
Clean grill grates and brush grates with olive oil.
Unroll the dough, cut it in half, and form to desired thickness and shape. Brush olive oil over the top of the dough (or flour that side of the dough) so it won't stick.
Place oiled (or floured) side of dough on the hotter side of grill for a few minutes, until top of dough blisters and bottom of the crust is cooked to your preference.
Flip the dough over and transfer it to the less hot side of the grill.
Spread a light layer of sauce over the dough, then sprinkle on the shredded cheese, to your preference.
Add any additional toppings, if desired.
Once your desired toppings are on the pizza, cook it until the crust is cooked to your taste and cheese is melted. Note: Extra toppings may require extra cook time, but be careful of overcooking the crust. Adjust heat as needed.
Remove from grill and let cool slightly. If desired, sprinkle on a little Parmesan cheese and Italian seasoning. Then cut pizza into slices or squares and serve.