Cool star atmospheres present challenges to chemical abundance studies. To date, only a handful of elements have been quantified for a handful of M dwarfs. In high-resolution spectra from the CARMENES survey, we identify a series of dramatically hyperfine-split vanadium features between 800 and 910 nm, which have strong and clean profiles throughout the early M-dwarf range. These 'bucket-shaped' line regions can be well-modeled with standard model atmospheres combined with the latest atomic data from VALD. From these line regions, we measure vanadium abundances for 140 nearby early M dwarfs in the CARMENES GTO sample and confirm that they follow the same trend with metallicity as the FG-type stars in the solar neighborhood, i.e., significantly above predictions from galactic chemical evolution models. Exhibiting a tight correlation with iron, vanadium abundances show promise as a potential metallicity indicator for M dwarfs. We also present evidence that several well-known chemical studies of K dwarfs have systematically overestimated their vanadium abundances largely as a result of neglecting to model hyperfine structure, a bias that worsens with decreasing temperature. Our work highlights opportunities for robust chemical analysis of cool stars afforded by high-quality spectra redward of visible.