The resonant absorption of light by an ensemble of absorbers decreases when the resonance is inhomogeneously broadened, as only a fraction of the ensemble contributes to the absorption at any given optical frequency. Recovering the lost absorption cross-section is of great importance for various applications of light-matter interactions, particularly in quantum optics and for few-photon nonlinearities. However, no recovery mechanism has yet been identified and successfully demonstrated. Here, we first formulate the limit set by the inhomogeneity on the absorption and then present a mechanism able to circumvent this limit and fully recover the homogeneous absorption of the ensemble. We experimentally study this mechanism using hot atomic vapor and demonstrate a 5-fold enhancement of the absorption above the inhomogeneous limit. Our scheme relies on light shifts induced by auxiliary fields and is thus applicable to various physical systems and inhomogeneity mechanisms.