Combine first 4 ingredients in a medium bowl; stir well. Cover and let stand at room temperature 5 minutes. Turn dough out onto a heavily floured surface, and knead 1 minute or until dough forms a smooth ball, adding more flour, if necessary. Divide dough in half.
Roll each portion of dough into a 12" x 10" rectangle; transfer dough to 2 baking sheets brushed with olive oil. (To transfer dough easily, roll dough onto rolling pin, and unroll onto baking sheets.) Roll or press each portion of dough into a 14" x 12" rectangle. (Dough should be very thin.) Brush each portion with 1 tablespoon olive oil; sprinkle evenly with cheese.
Bake at 425° for 10 minutes or until crispy and cheese is browned. Remove flatbread to wire racks, and let cool completely. To serve, break flatbread into large pieces. Store in an airtight container.