Better-Than-Pita Grill Bread

Whisk together flour (2 cups), sugar, salt, and yeast in a bowl until combined. Whisk together water, oil, and egg in another bowl until combined well, then stir into flour mixture until a shaggy dough forms. Turn out dough onto a lightly floured surface and knead, working in just enough additional flour to keep dough from sticking, about 2 minutes (dough will not be smooth). Form dough into a ball and put in an oiled bowl, turning to coat, then let rest in bowl, uncovered, in a warm draft-free place 10 minutes.

Cut dough into 10 pieces and form each into a ball. Working with 1 piece at a time, flatten balls, then roll out into 6-inch rounds (less than 1/8 inch thick) on lightly floured surface with a lightly floured rolling pin.

Preheat grill pan or skillet over moderately high heat just until smoking, then reduce heat to moderate and grill bread rounds, 1 at a time, turning once, until marks appear and bread is cooked through, about 2 minutes. Keep breads warm, wrapped in a cloth napkin.