When supercooled propylene carbonate and glycerol are subjected to a large-amplitude, low-frequency electric field, a spectral hole develops in their dielectric relaxation that is significantly narrower than their bulk response. This observation of nonresonant spectral hole burning establishes that the non-Debye response is due to a distribution of relaxation times. Refilling of the spectral hole occurs abruptly, indicative of a single recovery rate that corresponds to the peak in the distribution. The general shape of the spectral hole is preserved during recovery, indicating negligible interaction between the degrees of freedom that responded to the field. All relevant features in the behavior can be characterized by a model for independently relaxing domains that are selectively heated by the large oscillation, and which recover via connection to a common thermal bath, with no direct coupling between the domains.