Preheat a grill with coals on one half and bricks on the other (so that there is a hot and cool side). Assemble all of your topping ingredients on a big platter.
Lightly oil a sheet pan and roll and stretch one ball of dough until it is approximately 12-inches in length and 8-inches across. It is not necessary to make a perfect circle, but the dough should be an even thickness of 1/8-inch. Carefully stretch the dough onto the hot side of the grill and cook until the dough puffs on top, crisps on the bottom, and grill marks appear, about 1 to 2 minutes.
Flip the dough onto the cool side of the grill and brush the cooked side with olive oil. Quickly and sparingly assemble the toppings of your choice, such as tomato puree, fontina, and prosciutto di Parma, capers, and red peppers; or tomato puree, pecorino Romano, bel paese, grilled jumbo shrimp, and jarred Italian eggplant. Garnish with torn basil leaves. Feel free to improvise the toppings and come up with your own.
Once the pizza has been dressed, season it with salt and pepper, to taste, drag it over to the hot side of the grill, and cook until the ingredients are heated through. (If the pizza browns too quickly, pull it to the cool side and cover the grill to finish cooking.) Using a wide spatula or two pairs of tongs, carefully lift the pizza onto a cutting board and divide into 6 or 8 pieces. Serve right away. Repeat with the remaining dough.
Grilled Pizza Dough:
In a large bowl, combine the water, yeast, and molasses and stir gently to mix. Set aside for five minutes until bubbly and foamy. Add the salt, to taste, and oil and stir to mix.
In a separate bowl, whisk together the flours. Add the flours to the yeast mixture and stir with a wooden spoon until a dough forms and pulls away from the sides of the bowl.
Divide the dough into six equal pieces. Roll into balls and place on an oiled baking pan. Brush the balls with olive oil and cover with plastic wrap. Let rise in a warm place for 20 minutes.
When the grill is ready, oil a second baking sheet and flatten one ball of dough into a 10 to 12-inch piece about 1/8-inch thick. A perfect circle is less crucial than even thickness.
Cook's Note: Dough can be held for 1 day in the refrigerator. Let sit 1 hour at room temperature before grilling.