Our current understanding of supermassive black hole (SMBH) growth in the distant universe is compromised by the lack of key diagnostic rest-frame optical emission lines in the vast majority of quasar spectra. As a consequence, our view of how SMBHs and their host galaxies mutually coevolve during the peak of quasar activity is biased and incomplete. We are proposing to expand recent Gemini near-infrared spectroscopic observations and create the largest uniform inventory of rest-frame optical spectral properties of high-redshift quasars. We will observe the 0.8-2.5 um spectrum of 80 luminous sources at 3.2 < z < 3.5 which will provide, at a minimum, spectral properties of the Mg II 2796,2803A, Hb 4861A, Fe II 4434-4684A, and [O III] 5007A emission lines. All these sources have rest-frame ultraviolet spectra that provide information on the C IV 1549A emission line which will be utilized as a crucial calibrator. Together with the C IV data, the Gemini spectra will allow us to obtain the most accurate and precise quasar black hole masses, accretion rates, and redshifts, and we will use the results to derive improved prescriptions for ultraviolet-based proxies for these parameters that are crucial for a wide range of extragalactic investigations. We will make the raw data immediately available to the public and provide reduced spectra and spectral properties through the NOIRLab Astro Data Lab archive. Current large cosmological surveys are generating millions of optical quasar spectra, the analysis of which will greatly benefit from the prescriptions developed in this investigation, an invaluable Gemini legacy.