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Abstract We utilize ∼17,000 bright luminous red galaxies (LRGs) from the novel Dark Energy Spectroscopic Instrument Survey Validation spectroscopic sample, leveraging its deep (∼2.5 hr galaxy⁻¹exposure time) spectra to characterize the contribution of recently quenched galaxies to the massive galaxy population at 0.4 <z< 1.3. We useProspectorto infer nonparametric star formation histories and identify a significant population of recently quenched galaxies that have joined the quiescent population within the past ∼1 Gyr. The highest-redshift subset (277 atz> 1) of our sample of recently quenched galaxies represents the largest spectroscopic sample of post-starburst galaxies at that epoch. At 0.4 <z< 0.8, we measure the number density of quiescent LRGs, finding that recently quenched galaxies constitute a growing fraction of the massive galaxy population with increasing look-back time. Finally, we quantify the importance of this population among massive ( $\log \left(M_{\star }/M_{\odot }\right)$> 11.2) LRGs by measuring the fraction of stellar mass each galaxy formed in the gigayear before observation,f_{1 Gyr}. Although galaxies withf_{1 Gyr}> 0.1 are rare atz∼ 0.4 (≲0.5% of the population), byz∼ 0.8, they constitute ∼3% of massive galaxies. Relaxing this threshold, we find that galaxies withf_{1 Gyr}> 5% constitute ∼10% of the massive galaxy population atz∼ 0.8. We also identify a small but significant sample of galaxies atz= 1.1–1.3 that formed withf_{1 Gyr}> 50%, implying that they may be analogs to high-redshift quiescent galaxies that formed on similar timescales. Future analysis of this unprecedented sample promises to illuminate the physical mechanisms that drive the quenching of massive galaxies after cosmic noon.