Nanoparticles are known to self-assemble into larger structures through growth processes that typically occur continuously and depend on the uniformity of the individual nanoparticles. Here, we show that inorganic nanoparticles with non-uniform size distributions can spontaneously assemble into uniformly sized supraparticles with core-shell morphologies. This self-limiting growth process is governed by a balance between electrostatic repulsion and van der Waals attraction, which is aided by the broad polydispersity of the nanoparticles. The generic nature of the interactions creates flexibility in the composition, size and shape of the constituent nanoparticles, and leads to a large family of self-assembled structures, including hierarchically organized colloidal crystals.