Add water and sugar to the bowl of a standing mixer fit with a dough hook. Sprinkle in the yeast and let sit for 5 minutes to bloom.
Mix in the olive oil then Add one cup of the flour along with the salt. Mix on low until well incorporated, and then turn the speed up to medium and mix for 3 minutes.
Add another 1/2 cup of flour and the 1/2 cup of cornmeal, and mix well, starting on low and then switching to medium speed. Then add another 1/2 cup of flour, again starting on low and switching to medium. Knead on medium for about 5 minutes. You may occasionally have to get in there with your hands if the dough starts climbing up the hook. It should become smooth and elastic and slightly tacky. At this point, incorporate flour by the tablespoon, with the mixer running. When it starts to seem dry, stop adding flour. This could be anywhere between 1/4 and 1/2 cup. Knead again on medium until it is elastic easy to stretch, about 8 more minutes.
Meanwhile, drizzle about two tablespoons of olive oil into a large mixing bowl. The dough will double in size, so make sure you have enough room. Form the dough into a ball and place in the bowl, tossing it around to coat with oil. Cover the top in plastic wrap and put in a warm place. Let dough rise for about an hour, or until doubled in size.
When dough has doubled, fire up your grill. Keep the flame high and close the lid. If you have a thermometer, it should be at about 500 F.
Punch the dough down, give it a quick knead and tear it into 4 equal-ish pieces. On a large cutting board, form each piece into an oval that is about 8 inches long and 5 inches across. I just use my hands for this, but you can use a rolling pin if you prefer.
Place the dough on the grill. It should take about 3 to 4 minutes for the bottoms to get grill marks and become firm. If it takes a little longer that’s cool, but definitely check one after 3 minutes. Use tongs to flip the bread over and cook for another 2 minutes or so, until grill marks appear.
Remove breads from the grill with tongs and place on the large cutting board. Keep covered with a kitchen towel to keep warm until ready to use.