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To prepare the dough: Weigh your flour; or measure it by gently spooning it into a cup, then sweeping off any excess. In a large bowl or the bowl of a stand mixer fitted with the flat beater attachment, combine the flour, water, yeast, olive oil, and salt. Mix until a shaggy, sticky dough forms without any dry, floury patches. This should take less than 1 minute. Scrape down the sides to gather the dough into a rough ball. Cover and set aside.
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After 30 minutes, use a bowl scraper or your wet hand to grab a section of dough from one side, lift it up, and press it down to the middle to seal. Repeat, turning the bowl 90° between each stretch, until the dough won’t elongate easily, about 8 to 12 times total. This process, which is called a bowl fold, replaces kneading.
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Cover the bowl and let the dough rest at room temperature, undisturbed, for at least 30 minutes or for up to 3 hours. This forgiving dough will be fine with more or less time, but a longer rise will make shaping easier.
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Turn the dough out onto a lightly floured work surface. Gently deflate it and divide it in half (about 270g each).
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Shape each piece of dough into a rough ball by pulling the edges into the center. Turn the dough seam-side down, cover, and let rest for at least 20 minutes and up to 1 hour, until it’s relaxed enough to stretch.
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If using a gas grill, preheat to 350°F, then adjust some burners to medium-low and others to medium-high. If using a charcoal grill, set up two-zone grilling by banking the coals towards one side of the grill, which will create a hot and a less-hot section.
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To make the basting oil: In a small bowl, whisk together the olive oil and garlic. Set aside.
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To stretch the dough: Dust a pizza peel or thin wooden cutting board with semolina flour or cornmeal. (If you don’t have a pizza peel, you can shape and top the dough directly on parchment. You’ll then invert the dough onto the grill and peel back the parchment.) Transfer one ball of dough to the peel and sprinkle the top with flour. Use your fingertips to gently depress the round, stretching and pulling the dough gently into a 10" circle.
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To prepare the grill: Use a grill brush to remove any residue and clean the grates. For extra protection against sticking, use tongs to rub a wadded or folded paper towel coated in cooking oil over the grates.
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To grill the pizza: Lightly brush the shaped dough with the basting oil then transfer to the less-hot section of the grill and bake for 4 minutes, or until the bottom crust is golden brown. Keep the grill lid closed while baking, if possible. While the pizza cooks, shape your second round of dough.
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Remove the dough from the grill using a peel and gently flip it over, still on the peel, so that the cooked side is facing up. Off the heat, add your toppings: Scatter on sliced or torn mozzarella, followed by dollops of thick tomato sauce interspersed throughout (avoid covering the cheese). This topping sequence (cheese, then sauce) helps prevent a soggy crust. Place the pizza back on the grill, still in the less-hot section, and cook with the lid closed for an additional 4 minutes, or until the bottom crust is golden and the cheese is melted. Move your pizza towards the hotter section of the grill, as needed, for crispness and color. (To see this method in action, watch Martin grill a pizza .)
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Remove the pizza from the grill and brush the outer crust with basting oil, if desired. Slice and serve while still warm, then repeat the grilling process with your second pizza. (Alternatively, you can keep the first pizza warm on the upper rack of the grill or in a low-temperature oven, then serve both pizzas at once.)
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Storage information: Pizza is best eaten immediately. Store any leftovers in the refrigerator in an airtight container for up to three days.
