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