  The resolved mass assembly of Milky-Way-mass galaxies has been previously
studied in simulations, the local universe, and at higher redshifts using
infrared (IR) light profiles. To better characterize the mass assembly of Milky
Way Analogues (MWAs), as well as their changes in star-formation rate and color
gradients, we construct resolved stellar mass and star-formation rate maps of
MWA progenitors selected with abundance matching techniques up to z $\sim$ 2
using deep, multi-wavelength imaging data from the Hubble Frontier Fields. Our
results using stellar mass profiles agree well with previous studies that
utilize IR light profiles, showing that the inner 2 kpc of the galaxies and the
regions beyond 2 kpc exhibit similar rates of stellar mass growth. This
indicates the progenitors of MWAs from $z\sim 2$ to the present do not
preferentially grow their bulges or their disks. The evolution of the
star-formation rate (SFR) profiles indicate greater decrease in SFR density in
the inner regions versus the outer regions. S\'ersic parameters indicate modest
growth in the central regions at lower redshifts, perhaps indicating slight
bulge growth. However, the S\'ersic index does not rise above $n \sim 2$ until
$z < 0.5$, meaning these galaxies are still disk dominated systems. We find
that the half-mass radii of the MWA progenitors increase between $1.5 < z < 2$,
but remain constant at later epochs ($z < 1.5$). This implies mild bulge growth
since $z\sim 2$ in MWA progenitors, in line with previous MWA mass assembly
studies.
