Prepare Whole-Wheat Pizza Dough, if using. To cook pizzas on a charcoal grill, build a medium-hot fire in one half of the grill (two bricks placed end-to-end work well as a divider). For a gas grill with two burners, preheat one burner on high, leaving the other unlit. For a single-burner gas grill, preheat on high, and lower the flame to cook the second side of the pizzas.
Roll out the pizza dough into 4 circles and place on a floured cutting board. Bring the dough, toppings and a pair of tongs to grillside.
Place 2 of the dough circles on the hot side of the grill. Within 1 minute the dough will puff slightly, and the underside will firm up and be striped with grill marks. Use tongs to flip the crusts over and onto the cooler side of the grill.
Using half of the ingredients, spread olivada on the crusts after turning, then cover with overlapping tomato slices, sprinkle with salt and pepper and scatter mozzarella over all. Cover the grill and cook, rotating the pizzas once or twice, until the toppings are heated through, about 5 minutes.
Remove the pizzas from the grill. Repeat Steps 3 and 4 with the remaining dough and toppings. Just before serving, sprinkle the pizzas with basil.
If you don't have olivada (black olive spread), use a little prepared tomato sauce and scatter sliced olives over the top.
To make grating fresh mozzarella easier, place it in the freezer to firm up for about 20 minutes.