We have recently synthesized atomically flat semiconductor colloidal nanoplatelets with quasi 2D geometry. Here, we show that core/shell nanoplatelets can be obtained with a 2D geometry that is conserved. The epitaxial growth of the shell semiconductor is performed at room temperature. We report the detailed synthesis of CdSe/CdS and CdSe/CdZnS structures with different shell thicknesses. The shell growth is characterized both spectroscopically and structurally. In particular, the core/shell structure appears very clearly on high-resolution, high-angle annular dark-field transmission electron microscope images, thanks to the difference of atomic density between the core and the shell. When the nanoplatelets stand on their edge, we can precisely count the number of atomic planes forming the core and the shell. This provides a direct measurement, with atomic precision, of the core nanoplatelets thickness. The constraints exerted by the shell growth on the core is analyzed using global phase analysis. The core/shell nanoplatelets we obtained have narrow emission spectra with full-width at half-maximum close to 20 nm, and quantum yield that can reach 60%.