Strange phallic ice protrusion that grew on an ice cube in my freezer.
After some research, I discovered that it is a known physics phenomenon called "Ice Spike".
An ice spike is an upward-facing icicle that sometimes forms naturally as a body of water freezes.
Freezing causes water to expand, so it can force water out and upwards through a small hole in an already frozen surface sheet. This can produce a tube-like structure where water emerges at the tip, progressively lengthening the tube. Tube formation stops when the tip freezes and seals (from Wikipedia).
Ice Spikes happen more often with very pure water. San Francisco tap water is known to be very good quality.
View a more detailed explanation by Kenneth G. Libbrecht, Professor of Physics at Caltech and Chairman of the Physics Department.
And another page on ice spikes from the Dept. of Physics of University of Toronto.