For an experimental test see: Liquid marbles http://adsabs.harvard.edu/abs/2001Natur.411..924A
(paywall http://www.nature.com/nature/journal/v411/n6840/full/411924a0.html)
For a paper in General Relativity see: Accurate simulations of the dynamical bar-mode instability in full general relativity http://adsabs.harvard.edu/abs/2007PhRvD..75d4023B
Basically once you start increasing rotation the pancake will become unstable and will make a transition to a rotating bar (dumbbell).
Anyway I think that nobody ever saw the bar actually breaking into 2 pieces. Typically you loose matter from the external regions, redistribute angular momentum and go back to axisymmetry.
Cheers