  Phase transitions can modify quantum behaviour on mesoscopic scales and give
access to new and unusual quantum dynamics. Here we investigate the superfluid
properties of a rotating two-component Bose--Einstein condensate as a function
of changes in the interaction energy and in particular through the phase
transition from miscibility to immiscibility. We show that the breaking of one
of the hallmarks of superfluid flow, namely the quantisation condition on
circulation, is continuous throughout an azimuthal phase separation process and
displays intriguing density dynamics. We find that the resulting currents are
stable for long times and possess a phase boundary that exhibits classical
solid body rotation, despite the quantum nature of superfluid flow. To support
this co-existence of classical and quantum behaviour the system develops a
unique velocity flow profile, which includes unusual radial flow in regions
near the phase boundary.
