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International audience; We report on a novel method for the implementation of core-shell SiGe-based nanocrystals combining silicon on insulator dewetting in a molecular beam epitaxy reactor with an ex situ Ge condensation process. With an in situ two-step process (annealing and Ge deposition) we produce two families of islands on the same sample: Si-rich, formed during the first step and, all around them, Ge-rich formed after Ge deposition. By increasing the amount of Ge deposited on the annealed samples from 0 to 18 monolayers, the islands' shape in the Si-rich zones can be tuned from elongated and flat to more symmetric and with a larger vertical aspect ratio. At the same time, the spatial extension of the Ge-rich zones is progressively increased as well as the Ge content in the islands. Further processing by ex situ rapid thermal oxidation results in the formation of a core-shell composition profile in both Si and Ge-rich zones with atomically sharp heterointerfaces. The Ge condensation induces a Ge enrichment of the islands' shell of up to 50% while keeping a pure Si core in the Si-rich zones and a similar to 25% SiGe alloy in the Ge-rich ones. The large lattice mismatch between core and shell, the absence of dislocations and the islands' monocrystalline nature render this novel class of nanostructures a promising device platform for strain-based band-gap engineering. Finally, this method can be used for the implementation of ultralarge scale meta-surfaces with dielectric Mie resonators for light manipulation at the nanoscale.