Extrasolar Earth and super-Earth planets orbiting within the habitable zone of M dwarf host stars may play a significant role in the discovery of habitable environments beyond Earth. Spectroscopic characterization of these exoplanets with respect to habitability requires the determination of habitability parameters with respect to remote sensing. The habitable zone of dwarf stars is located in close proximity to the host star, such that exoplanets orbiting within this zone will likely be tidally locked. On terrestrial planets with an icy shell, this may produce a liquid water ocean at the substellar point, one particular "Eyeball Earth" state. In this research proposal, HABEBEE: exploring the HABitability of Eyeball-Exo-Earths, we define the parameters necessary to achieve a stable icy Eyeball Earth capable of supporting life. Astronomical and geochemical research will define parameters needed to simulate potentially habitable environments on an icy Eyeball Earth planet. Biological requirements will be based on detailed studies of microbial communities within Earth analog environments. Using the interdisciplinary results of both the physical and biological teams, we will set up a simulation chamber to expose a cold- and UV-tolerant microbial community to the theoretically derived Eyeball Earth climate states, simulating the composition, atmosphere, physical parameters, and stellar irradiation. Combining the results of both studies will enable us to derive observable parameters as well as target decision guidance and feasibility analysis for upcoming astronomical platforms.