Preheat grill to high heat. (Note: Something in the range of 450-500°F is ideal.)

On a lightly-floured countertop, roll the pizza dough out into a large circle. Sprinkle a pizza peel (or the bottom of a baking sheet) generously with cornmeal. Place the dough on the peel.

In a small dish, combine the pesto, salt, pepper and garlic; set aside.

Slide the dough on the grill, close cover and cook for 1-2 minutes. (Tip: Keep a close eye at this stage as the bottom of the dough can burn quickly!)

Flip the dough over and brush the pesto mixture evenly across the dough, leaving a 1” edge on all sides. Sprinkle the grated mozzarella cheese evenly across dough. Brush edges of the pizza with 1 Tbsp olive oil.

Close grill cover. Close air vents (on charcoal grill). (For gas, reduce temperature to medium.) Cook for 3-5 more minutes, or until cheese has fully melted and dough is fully cooked.

Using a large bowl, toss the diced tomatoes and chopped basil leaves with the remaining 1 Tbsp of olive oil.

Transfer pizza from grill onto a cutting board; immediately top pizza with the tomato/basil mixture. Finish by topping with fresh arugula and shaved Parmesan.