Carbon-enriched rocky exoplanets have been proposed to occur around dwarf stars as well as binary stars, white dwarfs, and pulsars. However, the mineralogical make up of such planets is poorly constrained. We performed high-pressure high-temperature laboratory experiments (P = 1-2 GPa, T = 1523-1823 K) on chemical mixtures representative of C-enriched rocky exoplanets based on calculations of protoplanetary disk compositions. These P-T conditions correspond to the deep interiors of Pluto- to Mars-sized planets and the upper mantles of larger planets. Our results show that these exoplanets, when fully differentiated, comprise a metallic core, a silicate mantle, and a graphite layer on top of the silicate mantle. Graphite is the dominant carbon-bearing phase at the conditions of our experiments with no traces of silicon carbide or carbonates. The silicate mineralogy comprises olivine, orthopyroxene, clinopyroxene, and spinel, which is similar to the mineralogy of the mantles of carbon-poor planets such as the Earth and largely unaffected by the amount of carbon. Metals are either two immiscible iron-rich alloys (S-rich and S-poor) or a single iron-rich alloy in the Fe-C-S system with immiscibility depending on the S/Fe ratio and core pressure. We show that, for our C-enriched compositions, the minimum carbon abundance needed for C-saturation is 0.05-0.7 wt% (molar C/O ∼0.002-0.03). Fully differentiated rocky exoplanets with C/O ratios more than that needed for C-saturation would contain graphite as an additional layer on top of the silicate mantle. For a thick enough graphite layer, diamonds would form at the bottom of this layer due to high pressures. We model the interior structure of Kepler-37b and show that a mere 10 wt% graphite layer would decrease its derived mass by 7%, which suggests that future space missions that determine both radius and mass of rocky exoplanets with insignificant gaseous envelopes could provide quantitative limits on their carbon content. Future observations of rocky exoplanets with graphite-rich surfaces would show low albedos due to the low reflectance of graphite. The absence of life-bearing elements other than carbon on the surface likely makes them uninhabitable.