Could the smell be from hot plastic?
Check the J1772 plug and receiver for signs of overheating, burn marks, deformation, etc.
If nothing looks amiss, start a charging. After 15 minutes or so, check for noticeable heat at the J1772 connection, the EVSE and the wall socket (if it is a plug in unit).
If not those, open the hood to find out if the smell is generated there.