  We investigate the assembly history of massive disk galaxies and describe how
they shape their morphology through cosmic time. Using SHARDS and HST data, we
modeled the surface brightness distribution of 91 massive galaxies at redshift
$0.14<z\leq 1$ in the wavelength range $0.5-1.6$ $\mu$m, deriving the
uncontaminated spectral energy distributions of their bulges and disks
separately. This spectrophotometric decomposition allows us to compare the
stellar populations properties of each component in individual galaxies. We
find that the majority of massive galaxies ($\sim85\%$) builds inside-out,
growing their extended stellar disk around the central spheroid. Some bulges
and disks could start forming at similar epochs, but these bulges grow more
rapidly than their disks, assembling $80\%$ of their mass in $\sim0.7$ Gyr and
$\sim3.5$ Gyr, respectively. Moreover, we infer that both older bulges and
older disks are more massive and compact than younger stellar structures. In
particular, we find that bulges display a bimodal distribution of mass-weighted
ages, i.e., they form in two waves. In contrast, our analysis of the disk
components indicates that they form at $z\sim1$ for both first and second-wave
bulges. This translates to first-wave bulges taking longer in acquiring a
stellar disk ($5.2$ Gyr) compared to second-wave less-compact spheroids ($0.7$
Gyr). We do not find distinct properties (e.g., mass, star formation timescale,
and mass surface density) for the disks in both types of galaxies. We conclude
that the bulge mass and compactness mainly regulate the timing of the stellar
disk growth, driving the morphological evolution of massive disk galaxies.
