  We develop a minimal model for \textit{pulsar glitches} by introducing a
solid-crust potential in the three-dimensional (3D) Gross-Pitaevskii-Poisson
equation (GPPE), which we have used earlier to study gravitationally bound
Bose-Einstein Condensates (BECs), i.e., bosonic stars. In the absence of the
crust potential, we show that, if we rotate such a bosonic star, it is threaded
by vortices. We then show, via extensive direct numerical simulations (DNSs),
that the interaction of these vortices with the crust potential yields (a)
stick-slip dynamics and (b) dynamical glitches. We demonstrate that, if enough
momentum is transferred to the crust from the bosonic star, then the vortices
are expelled from the star and the crust's angular momentum $J_c$ exhibits
features that can be interpreted naturally as glitches. From the time series of
$J_c$, we compute the cumulative probability distribution functions (CPDFs) of
event sizes, event durations, and waiting times. We show that these CPDFs have
signatures of self-organized criticality (SOC), which have been seen in
observations on pulsar glitches.
