We present spectroscopic observations of the dust-and gas-enshrouded, polluted, single white dwarf star SDSS J104341.53+085558.2 (hereafter SDSS J1043+0855). Hubble Space T elescope Cosmic Origins Spectrograph far-ultraviolet spectra combined with deep Keck HIRES optical spectroscopy reveal the elements C, O, Mg, Al, Si, P, S, Ca, Fe, and Ni and enable useful limits for Sc, Ti, V, Cr, and Mn in the photosphere of SDSS J1043+0855. From this suite of elements we determine that the parent body being accreted by SDSS J1043+0855 is similar to the silicate Moon or the outer layers of Earth in that it is rocky and iron-poor. Combining this with comparison to other heavily polluted white dwarf stars, we are able to identify the material being accreted by SDSS J1043+0855 as likely to have come from the outermost layers of a differentiated object. Furthermore, we present evidence that some polluted white dwarfs (including SDSS J1043+0855) allow us to examine the structure of differentiated extrasolar rocky bodies. Enhanced levels of carbon in the body polluting SDSS J1043+0855 relative to the Earth-Moon system can be explained with a model where a significant amount of the accreted rocky minerals took the form of carbonates; specifically, through this model the accreted material could be up to 9% calcium-carbonate by mass.