Roll out 1/2 your dough to 1/4-inch thick on a well-floured surface. Repeat with the other half of dough and set aside.
Heat grill to medium-high (450ºF-500ºF).
Brush one side with olive oil and place that side down on the flame-side of hot grill grates. Grill for about 5 minutes (the bottom will be crisped and fully cooked). Brush the top with oil and carefully flip!
Once flipped, quickly build the toppings on your pizza. Spread 1/2 the sauce on the bottom, then layer on 1/2 the mozzarella and basil.
Close the grill and let the bottom cook for another 3-5 minutes while the cheese melts on top. Remove from the grill once cooked through on the bottom and let cool.
Repeat with your second half of dough and toppings. Slice 'em up & serve!