Aside from my primary physician, who else can prescribe Propecia?

Any doctor or health care provider who can prescribe medication can prescribe Propecia.  A nurse practitioner, physician's assistant, or even a dentist can probably prescribe Propecia from a legal perspective.

Any medical doctor with a valid license in the state you live can likely prescribe this medication to men who are good candidates and don't have any contraindications (reasons on can't prescribe it). It is best to see a physician who can sit down with you are review all your medical history and go over all the potential side effects of this medication with you.

Anyone with who is a licensed medical doctor can prescribed Propecia (finasteride). There is not FDA substitute for finasteride, although a few other drugs have DHT blocking effects, the mechanism of action for this drug. 

any medical licensed physician can proscribe propecia. However it is better to make sure you are a candidate for it and also get familiar with the side effects before using it.