If the dough springs back when rolling it out, let the dough rest for a minute or two and continue rolling.
Place one dough round on a baking sheet sprinkled lightly with cornmeal. Sprinkle top lightly with cornmeal and top with a sheet of parchment paper. Continue with remaining flatbreads, sprinkling each with cornmeal and topping with parchment paper. Stack all four flatbreads. Cover whole stack with plastic wrap or foil and chill for up to 4 hours.