We have synthesized atomically flat CdSe/CdTe core/crown nanoplatelets (NPLs) with thicknesses of 3, 4, and 5 monolayers with fine control of the crown lateral dimensions. In these type-II NPLs, the charges separate spatially, and the electron wave function is localized in the CdSe core while the hole wave function is confined in the CdTe crown. The exciton's recombination occurs across the heterointerface, and as a result of their spatially indirect band gap, an important emission red shift up to the near-infrared region (730 nm) is observed with long fluorescence lifetimes that range from 30 to 860 ns, depending on the type of interface between the core and the crown. These type-II NPLs have a high quantum yield of 50% that can be further improved to 70% with a gradient interface. We have characterized these novel CdSe/CdTe core/crown NPLs using UV-vis, emission, and excitation spectroscopy, X-ray diffraction, energy-dispersive X-ray spectroscopy, and high-resolution transmission electron microscopy.