1 1/4 cups warm water (between 100 and 110 degrees), plus more as needed
1 small packet active dry yeast
1/2 teaspoon sugar
3 1/2 cups flour, plus more as needed and for the work surface
10 tablespoons olive oil, plus more for the bowl
2 teaspoons kosher salt, plus more as needed
Freshly ground black pepper
Toppings (see related story)
Combine the water, yeast and sugar in a small bowl, stirring to mix well; let sit for 10 minutes to allow the top to foam and become frothy (indicating that the yeast is active). If it does not do that, discard and start again with more water, yeast and sugar.
Lightly flour a work surface; lightly grease a mixing bowl and a rimmed baking sheet with a little olive oil.
Combine the flour, salt and 2 tablespoons of the oil in the bowl of a stand mixer fitted with the dough hook. Beat on low speed for 1 minute until well incorporated, then add the water-yeast mixture in a slow, steady stream. Beat for about 5 minutes, stopping to scrape down the sides of the bowl as necessary, until a dough forms and pulls cleanly from the sides of the bowl. Add a few tablespoons of water or flour if the dough is too dry or wet. Transfer the dough to the prepared work surface and knead for about 5 minutes, adding a little flour if it starts to stick, so the dough becomes smooth and elastic.
Transfer to the oiled bowl, cover with a clean, dry dish towel and let sit for 1 to 2 hours at room temperature, until the mixture almost doubles in size. Form the dough into 4 equal-size balls and place on the prepared baking sheet. (Alternatively, the dough may be wrapped tightly in plastic wrap and refrigerated for up to 2 days or frozen for up to 1 month.)
To roll out the dough balls, lightly flour a work surface. Line a large baking sheet with parchment paper, and have ready additional large sheets of the paper for stacking the rounds of dough.
Shape or roll one of the balls into a thin round between 10 and 12 inches in diameter. Brush the top side with 1 tablespoon of olive oil and flip the oiled side over onto the lined baking sheet. Brush the new top side of the dough with 1 tablespoon of the oil and cover with a piece of parchment paper. Repeat with the remaining 3 doughs and the oil. They may be held at room temperature for about 1 hour in this manner (or refrigerate, tightly covered, for up to 3 hours. If the dough has been refrigerated, let it sit at room temperature for 30 minutes to 1 hour, so it will be easier to stretch).
When ready to grill, build a two-zone fire. Heat the back 2 burners on a gas grill on HIGH and the front burners on LOW, or light a large charcoal fire and push most of the coals to one side of the grill, leaving a sparse layer of coals on the other side. When it has reached the right temperature, the hot zone of the fire should be so hot that you can hold your hand a couple of inches above the grill for only about 3 seconds (about 500 degrees, if using a surface thermometer). Clean the grill grates well and oil them lightly with a wad of paper towels.
Using both hands to hold the top of one of the dough rounds (as if your hands were at 10 and 2 on a steering wheel), gently lay the bottom part of the hanging dough on the far side of the hot zone and stretch the top toward you to the other side. Cook, without touching, for 1 minute, so the dough bubbles and starts to get good grill marks. Rotate 90 degrees and cook for 1 or 2 minutes, or until the dough is uniformly browned and crisp but has not burned.
Pull the dough to the cooler zone of the charcoal fire or to the front of the gas grill and reduce the heat on the middle zone of the gas grill to medium-low. Flip the dough over so the seared side faces up. Sprinkle toppings evenly over the pizza (remember, less is more; see related sidebar for topping suggestions).
Once the toppings are in place, cover the grill (with the vents open on a charcoal grill lid). Cook for 3 to 7 minutes, checking every minute or so to rotate the pie 90 degrees so it cooks evenly, until any cheese toppings melt. Transfer to a large cutting board to slice. Top and grill the remaining doughs in the same manner. Serve hot.
From food writer Tony Rosenfeld.