"Pizza on an outdoor grill is a great alternative to oven-cooked pizza. If you love crispy crust, this is for you. Note: cook time is relatively short, so alternative toppings like uncooked sausage or other meats may not cook fully."
Preheat grill to 600 deg F (or maximum possible temperature).
Allow dough to thaw (if frozen) and rise to 2-3 times original size. Divide in half and roll each out to 10-12" in size. Use flour to keep dough from sticking to roller and surface.
Using pizza peel (wooden paddle), transfer rounds to grill and close lid. cook 3-5 minutes, or until brown grill marks appear on bottom of round. Remove from grill and flip over. Lower grill temperature to 450 degrees F.
Brush top (already grilled) of each round lightly with oil.
Spread 2 ounces of sharp asiago on each round.
Add tomatoes, then basil on each round.
Spread 4 ounces fresh mozzarella on each round.
Add salt & pepper to taste.
Using pizza peel (wooden paddle), transfer rounds to grill and close lid. cook 7-10 minutes, or until brown grill marks appear on bottom of round and cheese is melted.
Remove from grill. Let pizza sit 5 minutes, then cut and serve.