Thermal emission from objects tends to be spectrally broadband, unpolarized, and temporally invariant. These common notions are now challenged with the emergence of new nanophotonic structures and concepts that afford on-demand, active manipulation of the thermal emission process. This opens a myriad of new applications in chemistry, health care, thermal management, imaging, sensing, and spectroscopy. Here, we theoretically propose and experimentally demonstrate a new approach to actively tailor thermal emission with a reflective, plasmonic metasurface in which the active material and reflector element are epitaxially grown, high-carrier-mobility InAs layers. Electrical gating induces changes in the charge carrier density of the active InAs layer that are translated into large changes in the optical absorption and thermal emission from metasurface. We demonstrate polarization-dependent and electrically controlled emissivity changes of 3.6%P (6.5% in relative scale) in the mid-infrared spectral range.