The observations from the Dark Energy Spectroscopic Instrument (DESI) will significantly increase the numbers of known extremely metal-poor stars by a factor of ∼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. [ABSTRACT FROM AUTHOR]