Grilled Pizza with Mozzarella, Arugula and Chile Oil

Dough: Put the warm water in a bowl and sprinkle the surface with the yeast. Let stand for 2 minutes, then whisk with a fork to blend. Let stand until bubbly, about 10 minutes. Whisk in the olive oil and salt, then gradually add 1½ cups of flour, beating with a wooden spoon until fully incorporated. The dough will be very moist and sticky.
Turn the dough out on a lightly floured work surface and knead with floured hands until smooth and elastic, about 5 minutes, incorporating as much of the remaining ¼ cup flour as needed to keep the dough from clinging to your hands or the work surface. The dough will remain moist and a little tacky but should not be sticky. Shape into a ball. Oil a bowl, transfer the dough to it, and turn the dough to coat it with oil. Cover the bowl with plastic wrap and let the dough rise at room temperature for 2 hours. Punch the dough down. Reshape into a ball, re-cover the bowl, and let the dough rise again for 4 hours.

If using a charcoal grill, prepare a moderate fire. When the coals are ready, arrange them in an even layer on one-half of the grill bed. For a gas grill, preheat all burners to high.15 minutes before grilling, put a baking stone on the grill rack. The internal temperature of the grill should be 575°F to 600°F.

Punch the dough down, turn it out onto a lightly floured work surface, and shape into a ball. Dust the surface of the dough with flour, cover with a dish towel, and let rest for 30 minutes.

Chile Oil: In a small bowl, whisk together the olive oil, garlic, hot pepper flakes, and salt. Add the oregano, crumbling it between your fingers, and whisk again. Let stand for 30 minutes to blend the flavors.

If using a charcoal kettle grill(round), shape the dough into a rectangle to cook the crust over direct heat, then flip and finish over indirect heat. For a gas grill with a baking stone, shape the dough into a circle as flipping isn't necessary.

Dust a pizza peel or rimless baking sheet generously with cornmeal. Stretch the dough, using a rolling pin or your hands into a 13-14 inch circle or 16x10 inch rectangle, depending on your grill. Transfer to the prepared peel/pan.

*If using a charcoal grill slide the dough off onto the grill rack, directly over the coals. Cook uncovered until the dough begins to puff and blister and the bottom becomes nicely browned or even lightly charred in spots, 1 to 2 minutes. With tongs or your hands, flip the dough over onto the half of the grill with no coals.

Working quickly, top with the cheese, spreading it evenly but leaving a ¾-inch rim uncovered. Brush the rim with the chile oil, then drizzle more of the oil, including the garlic and herbs, over the pizza, reserving a little oil for brushing the pizza rim after grilling. Cover the grill and cook until the pizza rim is well browned and the cheese is melted and bubbling, about 5 minutes. Transfer the pizza to a cutting board, scatter the arugula over the cheese, and brush the rim with the remaining chile oil. Cut into wedges and serve immediately.