Perovskite nanoparticles have attracted the attention of research groups around the world for their impressive photophysical properties, facile synthesis and versatile surface chemistry. Here, we report a synthetic route that takes advantage of a suite of soluble precursors to generate CsPbBr3 perovskite nanoplatelets with fine control over size, thickness and optical properties. We demonstrate near unit cell precision, creating well characterized materials with sharp, narrow emission lines at 430, 460 and 490 nm corresponding to nanoplatelets that are 2, 4, and 6 unit cells thick, respectively. Nanoplatelets were characterized with optical spectroscopy, atomic force microscopy, scanning electron microscopy and transmission electron microscopy to explicitly correlate growth conditions, thickness and resulting photophysical properties. Detailed in situ photoluminescence spectroscopic studies were carried out to understand and optimize particle growth by correlating light emission with nanoplatelet growth across a range of synthetic conditions. It was found that nanoplatelet thickness and emission wavelength increase as the ratio of oleic acid to oleyl amine or the reaction temperature is increased. Using this information, we control the lateral size, width and corresponding emission wavelength of the desired nanoplatelets by modulating the temperature and ratios of the ligand.