  We present a Bayesian full-spectral-fitting analysis of 75 massive ($M_* >
10^{10.3} M_\odot$) UVJ-selected galaxies at redshifts of $1.0 < z < 1.3$,
combining extremely deep rest-frame ultraviolet spectroscopy from VANDELS with
multi-wavelength photometry. By the use of a sophisticated physical plus
systematic uncertainties model, constructed within the Bagpipes code, we place
strong constraints on the star-formation histories (SFHs) of individual
objects. We firstly constrain the stellar mass vs stellar age relationship,
finding a steep trend towards earlier average formation with increasing stellar
mass of $1.48^{+0.34}_{-0.39}$ Gyr per decade in mass, although this shows
signs of flattening at $M_* > 10^{11} M_\odot$. We show that this is consistent
with other spectroscopic studies from $0 < z < 2$. This relationship places
strong constraints on the AGN-feedback models used in cosmological simulations.
We demonstrate that, although the relationships predicted by Simba and
IllustrisTNG agree well with observations at $z=0.1$, they are too shallow at
$z=1$, predicting an evolution of $<0.5$ Gyr per decade in mass. Secondly, we
consider the connections between green-valley, post-starburst and quiescent
galaxies, using our inferred SFH shapes and the distributions of galaxy
physical properties on the UVJ diagram. The majority of our lowest-mass
galaxies ($M_* \sim 10^{10.5} M_\odot$) are consistent with formation in recent
($z<2$), intense starburst events, with timescales of $\lesssim500$ Myr. A
second class of objects experience extended star-formation epochs before
rapidly quenching, passing through both green-valley and post-starburst phases.
The most massive galaxies in our sample are extreme systems: already old by
$z=1$, they formed at $z\sim5$ and quenched by $z=3$. However, we find evidence
for their continued evolution through both AGN and rejuvenated star-formation
activity.
