We investigate band-structure effects on the absorption spectra of quantum impurities in Dirac materials. We uncover the formation of novel quasiparticles – Dirac-Fermi polarons – emerging from the dressing of impurities by excitations near the Dirac point. These quasiparticles are remarkably robust, persisting for both attractive and repulsive interactions, and across the full range of electron and hole doping. We show that their spectroscopic signature is a generic feature of Dirac materials, accessible with established techniques in both solid-state and ultracold atomic platforms. Our results establish polaron spectroscopy as a powerful probe of Dirac points at energies far from the Fermi surface, providing direct access to band-structure effects beyond conventional approaches.

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