The day before making the pizza, remove the dough from the freezer. Place it on a plate or bowl. Spray plastic wrap with cooking spray and use this to cover the dough, with the sprayed side toward the dough. Place in refrigerator to thaw overnight.
The following day, remove the plate/bowl with dough from the refrigerator and allow it to come to room temperature, for at least an hour. The dough will rise slightly.
Prepare a large cutting board or similar surface with semolina flour. Transfer the dough to the prepared surface and dust some more flour on top. Take a knife and cut the dough into two portions. Reserve one of the portions for a separate pizza.
Using a rolling pin, begin rolling out one portion of the dough. Continue to dust with flour, roll out, turn over and roll again until it is the desired size. A rectangle or square shape works the best.
Preheat gas grill by turning on all burners to high and closing the lid as it preheats. If the grill has a temperature gauge, once it reads over 400 you should be good to go.
Take the entire cutting board out to the grill. Using two large spatulas transfer the pizza dough onto the hot grill. Leave the grill cover open and monitor the dough – it will only need about 2 minutes per side. Peek at the bottom of the crust using a spatula; if it looks slightly charred, it is time to flip. Using both spatulas, flip the dough over. The crust is now partially set and holds its shape. Let the second side cook for 2 minutes, then remove the crust from the heat and turn the burners down to medium.
Mix the sauce with the pesto and spread it on the crust. Add the rest of the toppings (except the arugulto the pizza. I prefer to add some of the shredded cheese first, then the veggies and fresh mozzarella, finishing with the rest of the cheese.
Once all ingredients are on the crust, transfer the pizza back to the grill. Close the lid and let the pizza bake for about 10-15 minutes. Check for “doneness” and adjust cooking time as needed.
Add arugula to the top of the cooked pizza.
Remove from heat, slice and serve.