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We describe an experimental concept at the National Ignition Facility for specifically tailored spherical implosions to compress hydrogen to extreme densities (up to $\sim$800$\times$ solid density, electron number density n$_e$$\sim$4$\times$10$^{25}$ cm$^{-3}$ ) at moderate temperatures (T$\sim$200 eV), i.e., to conditions, which are relevant to the interiors of red dwarf stars. The dense plasma will be probed by laser-generated x-ray radiation of different photon energy to determine the plasma opacity due to collisional (free-free) absorption and Thomson scattering. The obtained results will benchmark radiation transport models, which in the case for free-free absorption show strong deviations at conditions relevant to red dwarfs. This very first experimental test of free-free opacity models at these extreme states will help to constrain where inside those celestial objects energy transport is dominated by radiation or convection. Moreover, our study will inform models for other important processes in dense plasmas, which are based on electron-ion collisions, e.g., stopping of swift ions or electron-ion temperature relaxation.