We investigate the spectroscopic fingerprints of electron-plasmon coupling in integrated (PES) and angle-resolved photoemission spectroscopy (ARPES). To account for electron-plasmon interactions at a reduced computational cost, we derived the plasmonic polaron model, an approach based on the cumulant expansion of many-body perturbation theory that circumvents the calculation of the GW self-energy. Through the plasmonic polaron model, we predict the complete spectral functions and the effects of electron-plasmon coupling for Si, Ge, GaAs, and diamond. Si, Ge, and GaAs exhibit well-defined plasmonic polaron band structures, i.e., broadened replica of the valence bands redshifted by the plasmon energy. Based on these results, (i) we assign the structures of the plasmon satellite of silicon (as revealed by PES experiments) to plasmonic Van Hove singularities occurring at the L, $Ω$, and X high-symmetry points and (ii) we predict the ARPES signatures of electron-plasmon coupling for Si, Ge, GaAs, and diamond. Overall, the concept of plasmonic polaron bands emerges as a new paradigm for the interpretation of electronic processes in condensed matter, and the theoretical approach presented here provides a computationally affordable tool to explore its effect in a broad set of materials. ; Comment: 7 pages, 4 figures