Adding A New Method to Viewlet Manager?

If you inspect with @@manage_viewlets, you'll see that part is already a viewlet. You've just to override its view and template using zcml:

https://5.docs.plone.org/develop/plone/views/more_view_examples.html#overriding-the-title

Instead of the Title viewlet, override the plone.personal_bar viewlet class to implement the method to get the portrait url and the template to display it as outlined here: