We report on a new formalism for parton showers whose fixed-order
expansion can be corrected through next-to-next-to-leading order
(NNLO) in QCD. It is the first such formalism we are aware of that has
no dependence on any auxiliary scales or external resummations and
which is fully differential in all of the relevant phase
spaces. Since the shower acts as the phase-space generator, the
dominant singularity structures are encoded by construction and the
method is capable of generating unweighted events with very high
efficiency without any significant initialisation time. We argue that
the the method should be capable of achieving (at least) NNLO+NNDL accuracy for the shower evolution variable, and use hadronic 𝑍 decays as a specific example.