Prepare a medium-low fire in the grill.

In a medium bowl, combine the yeast with the water and corn syrup and let rest for 10 minutes, until foamy. Stir in about 3 cups of the flour and add the salt. Add the remaining cup of flour a few tablespoons at a time, adding it only until you have a sticky dough. Transfer the dough to a floured surface and divide into six equal portions.

Flour your hands generously and, with your fingertips, press and pull each portion until it is an oval about 5 inches wide and 7 inches long. Dust each oval lightly with flour. Stack on a plate with a piece of oiled parchment between each oval. At this point, the plate of flatbreads can be tightly wrapped in foil and refrigerated about 2 hours.

When you are ready to cook, brush both sides of each oval lightly with olive oil. Dip your fingertips into water and press down into the dough to create small indentations. Sprinkle each oval with sesame seeds and/or rosemary.

Arrange the breads on the hot grate over medium-low coals and grill for about 4 minutes, until the side on the grill is golden and crusty. Flip the flatbreads and cook the other side for 4 minutes.

Transfer breads to a serving platter and serve warm.