Unroll breadstick dough on work surface. Cut dough in half crosswise, and separate to make 16 strips; cut each of the strips in half lengthwise to make 32 thin strips. Place strips on cookie sheets, 1 inch apart. Using a small paring knife or kitchen scissors, make 4 thin cuts (2 inches long) on 1 end of each strip. Spread out cut ends to make bristles of each broom. Brush dough with oil; sprinkle with Parmesan cheese.