Measure out 1 cup of warm water (it should be pleasantly warm on your wrist). Sprinkle the yeast on top of the water and allow it to activate, about 10 minutes. Put the salt and 2 cups of the flour into a food processor. Pulse 5 times to blend. Pour in the yeast and water and pulse 5 times. Add the olive oil. Next, add the remaining flour 1 cup at a time, pulsing and scraping the sides of the bowl until well blended. As soon as the mixture is combined, dump it out onto a well-floured board and knead for 15 turns, until the dough is smooth and elastic.
Place the dough in a greased bowl and turn to coat all sides. Cover with plastic wrap or a tea towel. Allow the dough to rise in a warm place for about 1 hour, until doubled in size, and then punch it down. Divide it in half; each half will make 1 (12-inch) pizza.
Shape the pizza dough by flattening it with your hands on a slightly floured surface. Either use your fingers to stretch the dough out, or hold up the edges of the dough with your fingers, letting the dough hang and stretch, while working around the edges of the dough. Once you've stretched the dough, let it sit for 5 minutes and then push out the edges with your fingers again, until you have a nice round shape, about 12-inches in diameter. Do not make a raised rim, it will interfere with the grilling process.
In a large heavy saucepan sauté the garlic in the oil over moderately low heat, stirring, for 2 minutes, or until the mixture is fragrant. Add the following spices: paprika, garlic, onion, salt, black pepper and sugar. Sauté for 1 additional minute then add tomato sauce and cook it over moderately low heat, stirring occasionally for about 20 minutes.
Once the grill is hot (you can hold your hands an inch over the grates for no more than 2 seconds), dip a tightly folded up paper towel in olive oil and use tongs to wipe the grill grates. Then place a pizza dough round on a lightly floured flat baking sheet. Let the dough slide off the cookie sheet onto the hot grill. Close the lid and grill for approximately 2 minutes or until bottom has become browned.
Remove the pizza from the grill back to the baking sheet. Brush the cooked surface of the pizza with a little olive oil, then lightly cover with tomato sauce not a lot, or you'll end up with a soggy pizza. Sprinkle on thePizza Spice Seasoningand Mozzarella cheese, and if using meat, put that over the cheese. Remember to go light on the toppings, or your pizza will be heavy and soggy.
Close the lid and cook for 2-3 minutes more, or until the bottom begins to char and the cheese is bubbling. Pull off the grate with a spatula onto a cutting board or other flat surface and let rest for a couple minutes before cutting into slices.