1. Heat 2 tablespoons of olive oil in a medium sauté pan over medium-low heat.
2. Add anchovies and onion and sauté until onion is translucent, 8-10 minutes.
3. Add olives and capers and cook for 1 minute more to combine flavors.
4. Transfer mixture to a bowl.
5. In a medium bowl, crush tomatoes with your hands, and stir in basil, garlic, salt & pepper. Set up olive mixture, crushed tomato sauce, parmagiano, and olive oil at your grilling station for easy access.
6. Prepare a charcoal grill for grilling pizza creating a very hot fire on one side with a couple of layers of charcoal just a few inches from the grate, and a low fire on the other side with just a few coals.
7. Oil the bottom of a baking sheet and place one of the dough balls on it.
8. Using your hands flatten it out to about 1/8 inch thick.
9. Carefully slide the dough onto the hot side of the grill.
10. Watch the dough closely making sure it doesn't burn by lifting it with tongs and peeking under.
11. When the dough is charred on the bottom, flip it over and brush it with olive oil and quickly sprinkle with Parmigiano-Reggiano.
12. Next use tongs or your hands to place the tomatoes over the surface, trying not to take too much of the juices with them. 13. Finally, top with strategically placed dollops of olive, caper and onion mixture.
14. With either the tongs or a spatula, slide the pizza to the cooler side of the grill, cover making sure the vent holes are open and cook for 3-5 more minutes.
15. The pizza is done when the toppings are heated through and the bottom is slightly charred.
16. Using a spatula, remove pizza from grill to a serving tray, slice and serve.
17. Repeat with second ball of dough.