The search for sterile neutrinos is perhaps the brightest possibility in our quest for understanding the microscopic nature of the observed dark matter (DM) in our Universe. Sterile neutrinos – unlike the active neutrinos in the Standard Model – do not interact with normal matter as they move through space, and are thus best observed using their mass signature. In this work, complete momentum reconstruction of electron-capture (EC) nuclear decay is employed to perform a search for sterile neutrinos in the keV mass range that is 10,000 times more sensitive than previous experiments. This is achieved using the EC decay of radioactive beryllium-7 atoms implanted into sensitive superconducting tunnel junctions (STJs) – an experiment nicknamed the BeEST (beast) for Beryllium Electron capture in STjs. A discovery signature in the BeEST experiment would be a small fraction of these decays where the daughter (lithium-7) atomic recoil peaks are shifted to lower energies from momentum conservation with these new, heavy sterile neutrinos. This approach is a uniquely powerful experimental method since it relies only on the well-motivated existence of this new type of neutrino, and not on how they might hypothetically interact with normal matter.