Replacing a microwave door handle is simpler then you might think.
Open the microwave door, the thin one inch wide trim piece that goes all the way around the door will need to be removed out of place. This piece is called the “choke” and it acts as the door seal around the border of the inside door liner.
Putty knives work the best to get under the plastic, this allows the trim to be pried out of position. With the small trim removed the two handle mounting screws are visible.
The broken end of the handle may be lodged inside the door, this will cause the screw to keep spinning, using needle nose pliers hold the broken plastic piece and remove the screw. Fasten the new handle to the microwave door and replace the trim. Test the microwave operating function closing and opening the door several times.