Free standing two-dimensional materials appear as a novel class of structures. Recently, the first colloidal two-dimensional heterostructures have been synthesized. These core/shell nanoplatelets are the first step toward colloidal quantum wells. Here, we study in detail the spectroscopic properties of this novel generation of colloidal nanoparticles. We show that core/shell CdSe/CdZnS nanoplatelets with 80% quantum yield can be obtained. The emission time trace of single core/shell nanoplatelets exhibits reduced blinking compared to core nanoplatelets with a two level emission time trace. At cryogenic temperatures, these nanoplatelets have a quantum yield close to 100% and a stable emission time trace. A solution of core/shell nanoplatelets has emission spectra with a full width half-maximum close to 20 nm, a value much lower than corresponding spherical or rod-shaped heterostructures. Using single particle spectroscopy, we show that the broadening of the emission spectra upon the shell deposition is not due to dispersity between particles but is related to an intrinsic increased exciton-phonon coupling in the shell. We also demonstrate that optical spectroscopy is a relevant tool to investigate the presence of traps induced by shell deposition. The spectroscopic properties of the core/shell nanoplatelets presented here strongly suggest that this new generation of objects will be an interesting alternative to spherical or rod-shaped nanocrystals.