Prepare a grill for medium heat cooking.

Mix tomatoes with garlic, 2 tablespoons of the olive oil and salt and set aside.

Working on a lightly floured surface, divide dough into 3 balls, then flatten each and dust all over with flour.

Hold up 1 ball of dough by its edge and turn it, steering-wheel-style, letting gravity stretch it into a 7-inch circle.

Lay it on the work surface and stretch it to form an 8-inch circle.

Set aside and repeat with remaining dough.

Working in batches if needed, brush dough with some of the remaining oil.

Lay it on the grill, oiled-side down, and brush the other side with oil.

Grill until the bottom browns, about 3 minutes.

Using a spatula and tongs, flip the crust and top with reserved tomato mixture, sausage, mozzarella and arugula, leaving a thin border around the edge.

Close the grill lid, or cover pizza with a tent of heavy foil, and cook until crust turns golden on bottom and cheese melts, about 2 minutes.

Remove from the grill and sprinkle with Parmesan cheese.

Cut pizzas into quarters to serve.