We address the oversight of many body interactions in dark matter admixed neutron stars (DMANS) by including Brueckner-Hartree-Fock (BHF) informed nucleon effective mass in zero temperature. Using the dark matter admixed chiral sigma model with new DM-hadron mediators we examine the modified equations of state and macroscopic properties of NS in static and slowly rotating cases. Such corrections lead to significant deviation from solely effective field theory considerations. We also show that the high energy density behavior of the speed of sound in BHF scenario is more consistent than the EFT scenario with Bayesian analysis of experimental results.