  Within perturbative QCD, we develop a new picture for the parton shower
generated by a jet propagating through a dense quark-gluon plasma. This picture
combines in a simple, factorised, way multiple medium-induced parton branchings
and standard vacuum-like emissions, with the phase-space for the latter
constrained by the presence of the medium. We implement this picture as a Monte
Carlo generator that we use to study two phenomenologically important
observables: the jet nuclear modification factor $R_{AA}$ and the $z_g$
distribution reflecting the jet substructure. In both cases, the outcome of our
Monte Carlo simulations is in good agreement with the LHC measurements. We
provide basic analytic calculations that help explaining the main features
observed in the data. We find that the energy loss by the jet is increasing
with the jet transverse momentum, due to a rise in the number of partonic
sources via vacuum-like emissions. This is a key element in our description of
both $R_{AA}$ and the $z_g$ distribution. For the latter, we identify two main
nuclear effects: incoherent jet energy loss and hard medium-induced emissions.
As the jet transverse momentum increases, we predict a qualitative change in
the ratio between the $z_g$ distributions in PbPb and pp collisions: from
increasing at small $z_g$, this ratio becomes essentially flat, or even
slightly decreasing.
