Remove the existing flooring in the doorway if you have not done so already.
Lay the scrap piece of underlayment down in the doorway. Lay the scrap piece of hardwood down directly on top of the underlayment in the doorway.
Mark both sides of the door frame with a pencil where the board hits the frame.
Press the scrap piece of hardwood against the door frame. Position your saw directly on top of the scrap plank. Cut the door frame away where the plank meets the frame. Do this on both sides of the door frame.
Measure the width of the doorway. Cut a wooden floor plank to fit horizontally within the door frame.
Install the hardwood plank in the doorway. Provided you measured and cut the door frame correctly, the plank should sit comfortably within the doorway.