  Traversing a continuous phase transition at a finite rate leads to the
breakdown of adiabatic dynamics and the formation of topological defects, as
predicted by the celebrated Kibble-Zurek mechanism (KZM). We investigate
universal signatures beyond the KZM, by characterizing the distribution of
vortices generated in a thermal quench leading to the formation of a
holographic superconductor. The full counting statistics of vortices is
described by a binomial distribution, in which the mean value is dictated by
the KZM and higher-order cumulants share the universal power-law scaling with
the quench time. Extreme events associated with large fluctuations no longer
exhibit a power-law behavior with the quench time and are characterized by a
universal form of the Weibull distribution for different quench rates.
