The observations from the Dark Energy Spectroscopic Instrument (DESI) will significantly increase the numbers of known extremely metal-poor stars by a factor of similar to 10, improving the sample statistics to study the early chemical evolution of the Milky Way and the nature of the first stars. In this paper we report follow-up observations with high signal-to-noise ratio of nine metal-poor stars identified during the DESI commissioning with the Optical System for Imaging and Low-Resolution Integrated Spectroscopy (OSIRIS) instrument on the 10.4 m Gran Telescopio Canarias. The analysis of the data using a well-vetted methodology confirms the quality of the DESI spectra and the performance of the pipelines developed for the data reduction and analysis of DESI data.