We present the synthesis and the optical properties of a new type of two-dimensional heterostructure: core/crown CdSe/CdS nanoplatelets. They consist of CdSe nanoplatelets that are extended laterally with CdS. Both the CdSe core and the CdS crown dimensions can be controlled. Their thickness is controlled at the monolayer level. These novel nanoplatelet-based heterostructures have spectroscopic properties that can be similar to nanoplatelets or closer to quantum dots, depending on the CdSe core lateral size.