Astrophysical collisionless shocks are among the most powerful particle accelerators in the Universe. Generated by violent interactions of supersonic plasma flows with the ambient medium, shock waves are observed to amplify magnetic fields and to accelerate electrons and ions to highly relativistic speeds. Recent developments in laboratory high-energy-density (HED) laser-plasma experiments are now opening for the first time the opportunity to probe the microphysics and particle acceleration mechanisms of magnetized collisionless shocks in conditions relevant to high-energy astrophysical environments. The goal of this ASCR Leadership Computing Challenge proposal is to perform large-scale first-principles fully-kinetic simulations of magnetized collisionless shocks in HED laboratory plasmas that will be critical to support Discovery Science experiments at the National Ignition Facility that have been approved and are currently planned. The fundamental understanding of particle acceleration in plasmas provided by this project is central to DOE’s mission in Discovery Plasma Science. The results of this research are expected to have a significant impact on unveiling long-standing questions behind cosmic plasma accelerators, in advancing the understanding of interpenetrating magnetized HED plasmas, and in generating new ideas for efficient laboratory accelerators. Finally, the tight connection between the proposed simulations and experimental programs on NIF will also enable the important benchmark of widely used numerical plasma models in magnetized HED conditions of relevance to DOE programs.