Lightly flour the back of a 15-by-10-inch baking sheet. Roll or pull the pizza dough to about 1/2 inch thick. Place the dough on the back of the baking sheet. Brush liberally with olive oil.
Light a charcoal grill and allow the coals to burn until covered with gray ash or heat a gas grill to medium. Using the baking sheet like a big spatula, slide the dough directly onto the cooking grate. Grill over direct medium heat until the underside of the dough is marked, 1 to 3 minutes. Don't worry if the crust bubbles; it will deflate when turned over. Slide the dough onto the baking sheet and flip the ungrilled side onto the grate.
Brush with olive oil and scatter the cheddar, rosemary, and salt on top. Cover and grill for 2 to 3 minutes. Remove the flatbread from grill and cool slightly on a rack. Cut cross-wise into strips. Can be served at room temperature.