  The bulk of the present-day stellar mass was formed in galaxies when the
universe was less than half its current age (i.e., $1 \lesssim z \lesssim 3$).
While this likely marks one of the most critical time periods for galaxy
evolution, we currently do not have a clear picture on the radial extent and
distribution of cold molecular gas and associated star formation within the
disks of galaxies during this epoch. Such observations are essential to
properly estimate the efficiency at which such galaxies convert their gas into
stars, as well as to account for the various energetic processes that govern
this efficiency. Long-wavelength (i.e., far-infrared--to--radio) observations
are critical to penetrate the high-levels of extinction associated with dusty,
infrared-bright galaxies that are driving the stellar mass assembly at such
epochs. In this article we discuss how the next-generation Very Large Array
will take a transformative step in our understanding of galaxy formation and
evolution by delivering the ability to simultaneously study the relative
distributions molecular gas and star formation on sub-kpc scales unbiased by
dust for large populations of typical galaxies in the early universe detected
by future far-infrared space missions.
