We present the synthesis of novel disk-shaped hexagonal Cu2_{Te nanocrystals with a well-defined stoichiometric composition, and tunable diameter and thickness. Subsequent cation exchange of Cu to Cd at high temperature (180 °C) results in highly fluorescent CdTe nanocrystals, with less than 1 mol.% of residual Cu remaining in the lattice. The procedure preserves the overall disk shape, but is accompanied by a substantial reconstruction of the anion sublattice, resulting in a reorientation of the c-axis from the surface normal in Cu}2_{Te into the disk plane in CdTe nanodisks. The synthesized CdTe nanodisks show a continuously tunable photoluminescence (PL) peak position, scaling with the thickness of the disks. The PL lifetime further confirms that the CdTe PL arises from band-edge exciton recombination, i.e. no Cu-related emission is observed. On average, the recombination rate is about 25-45% faster with respect to their spherical quantum dots counterparts, opening up the possibility to enhance the emission rate at a given wavelength by controlling the nanocrystal shape. Finally, with a PL quantum efficiency of up to 36% and an enhanced PL stability under ambient conditions due to a monolayer of CdS formed on the nanocrystal surface during cation exchange, these flat quantum disks form an interesting enrichment to the current family or highly fluorescent, shape-controlled nanocrystals.}