Metal-enriched white dwarfs provide a unique insight into the composition of exoplanet interiors. These stars accrete the debris of disrupted planetary bodies, and hence, measuring the stellar parameters and photospheric abundances yields the bulk compositions of the parent bodies. At present, over 1750 debris-accreting white dwarfs are known, but just a few dozen are sufficiently enriched to allow a detailed abundance study. Here, we report the analysis of 12 highly metal-enriched white dwarfs observed within the Data Release 1 of the Dark Energy Spectroscopic Instrument (DESI). We characterized their stellar parameters and photospheric metal abundances, and we identified between three and ten different elements in their optical spectra, including most of the rock-forming species: O, Mg, Si, Ca, and Fe. We conclude that the accreted bodies broadly resemble compositions found within the inner Solar system such as primitive meteorites, processed material, or planetary cores. Six of the systems allowed a more thorough analysis: four of the parent bodies are composed of dry rock-forming elements; and two of them of something akin to a water-rich planetesimal. Thus, this study establishes DESI as a potent survey for identifying metal-rich targets, yielding reliable compositions of accreted exoplanetary material.