OK, so let's investigate. First, a walk down the street. Oh, no! Next door's nature-strip prunus has the same odd outgrowth; but in two or three places. Are we descending into a strange world of Edward Lear-like Bong trees where the leaves of one grow on another completely different type? Evergreen leaves on a deciduous tree? Or is there something more sinister at work? I never read much science fiction but I did read all of John Wyndham.
Now let's climb. The parasite appears to have germinated in forks of the tree. These very old prunus are subject to attack by borers of some kind, which leave small deposits that take on a muddy consistency after rain. This mud lodges in the forks. Let's presume it provides a fertile medium for germination. Closer inspection reveals tendrils encircling the bough below the infestation. Hybrid roots? Perhaps. My correspondent, Melbourne Girl, suggested Mistletoe of some kind. But does mistletoe have exterior roots or invade its host bough?
Time to take a cutting and make further enquiries. At least I know I'm not hallucinating. I think.