Use the grill outfitted with a baking stone to get higher temps thanmost ovens, and in turn a crisp-bottomed but chewy crust. An overturned heavy-duty sheet pan, preheated in the grill or oven, will also work. Roma tomatoes contain less water and won’t make the crust soggy. The freshmozzarella can be drained of some of its liquid sliced and set on paper towels,but I tried it both ways and the cheese was not soggy on the pizza even when itwas not drained. The dough can be made, of course, by hand, but I found thedough dramatically more beautiful, softer and stickier (which like pizza dough,is better for flatbread) made in the food processor fitted with the metalblade. This recipe is based on Barbara Abdeni Massaad’s Man’oushe. Great as appetizers or with a green salad for a meal.
In a large bowl or the bowl of a food processor, combine the flours and salt. Whisk together if making by hand; pulse a few times if using the processor.
Proof the yeast in a small bowl. Mix the yeast and sugar together, then slowly add ¼ cup of thelukewarm water while stirring to combine. Set aside for 15 minutes until the yeast is foamy.
Add the yeast mixture and the tablespoon of oil to the flour mixture. Mixing by hand, or with the food processor running, slowly pour in the remaining cup of warm water. Mix until combined and knead, if by hand, for 10 minutes until the dough is soft and elastic. If using the processor, run for a full minute after the water is added. The dough will form a ball and turn in the bowl as the machine runs.
Set the dough to rise by placing the dough in a bowl that is completely but lightly oiled, and turn the dough so it is entirely coated with oil too. Cover the bowl with plastic wrap and then a kitchen towel and place in a warm spot until doubled in size, 1 ½-2 hours.
Gently remove the dough from the bowl and divide into four evenly sized balls. Set the balls on a lightly floured surface and coat lightly with more flour. Cover with the plastic wrap and kitchen towel and rise for 20 minutes.
Meanwhile, preheat the grill with the pizza stone, top closed, at high heat.If using the oven, place the baking stone in the bottom of the oven. Remove the racks or line them at the top of the oven. Heat the oven to 400 degrees for20-30 minutes. Convection baking is ideal here, if possible. If you’re using convection, set the oven temperature to 425 degrees.
Roll out the dough: lightly flour the work surface, the rolling pin, and the peel (or another overturned sheet pan to be used as a peel like a huge spatula). The flour acts as ball bearings for the dough to keep it from sticking to surfaces. Place one ball of dough on the floured surface and press down on it with the palm of your hand. The key to getting the dough rolled flat and round is to keep it moving, which means turning it frequently throughout the rolling process and adding more flour lightly to the work surface as yougo. Roll the dough from the center of the circle to the edge a couple of times,then rotate it, and roll again, repeating until the dough is round and ¼ -inch thick. If you like a thicker pizza, roll to ½-inch thick.
Coat the pizza peel liberally with flour. Gently transfer the rolled dough to the peel before adding the toppings. Brush the entire surface of the dough with olive oil. Mix all but a couple of teaspoons of the za'atar with all but a couple of teaspoons of the oil. Spread this mixture over the dough using the back of a spoon or your fingers, leave a ½ -inch rim around the edge. Top with tomato slices and mozzarella. Coat the perimeter of the dough with the remaining olive oil and dust the top of the pizza with the remaining za'atar. Slide the peel under the dough, using two hands (to avoid misshaping the round) to pull the dough onto the floured peel. Place on the baking stone and grill (or bake) 5-7 minutes, or until the bottom of the crust is golden and the top is bubbly and golden.
Repeat the process with each of the four balls of dough.