[en] Recently, a new non-Standard Model neutrino interaction mediated by a light scalar field was proposed, which renders the big-bang relic neutrinos of the cosmic neutrino background a natural dark energy candidate, the so-called Neutrino Dark Energy. As a further consequence of this interaction, the neutrino masses become functions of the neutrino energy densities and are thus promoted to dynamical, time/redshift dependent quantities. Such a possible neutrino mass variation introduces a redshift dependence into the resonance energies associated with the annihilation of extremely high-energy cosmic neutrinos on relic anti-neutrinos and vice versa into Z-bosons. In general, this annihilation process is expected to lead to sizeable absorption dips in the spectra to be observed on earth by neutrino observatories operating in the relevant energy region above 10¹³ GeV. In our analysis, we contrast the characteristic absorption features produced by constant and varying neutrino masses, including all thermal background effects caused by the relic neutrino motion. We firstly consider neutrinos from astrophysical sources and secondly neutrinos originating from the decomposition of topological defects using the appropriate fragmentation functions. On the one hand, independent of the nature of neutrino masses, our results illustrate the discovery potential for the cosmic neutrino background by means of relic neutrino absorption spectroscopy. On the other hand, they allow to estimate the prospects for testing its possible interpretation as source of Neutrino Dark Energy within the next decade by the neutrino observatories ANITA and LOFAR. (Orig.)