In this work, we share the discovery and characterization of three mini-quenched galaxies at z=4-6, discovered in the spectroscopic component of the UNCOVER survey (JWST observations of Abell 2744; PIs Bezanson, Labbe). We find these galaxies with their characteristic features -- bright rest-frame UV flux, a weak Balmer/4000A break, and weak or absent emission lines -- corresponding to residual star formation and presence of old stellar populations. We constrain the star formation histories in these systems with flexible non-parametric models via Prospector, which indicate the delensed stellar masses of the sample to be in the range logM= 8.5-9.5, highlighting for the first time a more massive “napping” galaxy. The specific star formation rates of these mini-quenched galaxies place them below the star formation main sequence. The posterior distributions of the time-averaged SFRs show that these systems are outliers in the SFR10/SFR100 parameter space. We demonstrate that this class of galaxies can best be identified and characterized spectroscopically due to the challenge of photometrically capturing the UV flux, weak Balmer/4000A break, and weak emission lines simultaneously.