Anyone know the purpose of these two inductors around a metallic ring?
The board does two things.  It protects the microwave from shorts, electrical noise, and line faults such as voltage spikes.  It also protects the line from noise the microwave generates.

The wires wrapped around the metal toroid form an inductor.  This is to prevent electrical noise the microwave generates transferring to the powerline, and electrical noise on the powerline from transferring to the microwave.  It's done primarily in order to meet emissions requirements (in the US the FCC regulates this), but also to prevent line noise from affecting microwave operation.

You can read more about noise suppression ferrites here:

http://audiosystemsgroup.com/SAC0305Ferrites.pdf