The combination of high spectral and spatial resolution (of order R = 100,000 and 1 mas, respectively) at the VLTI would open new vistas in stellar astrophysics, with important applications to planetary systems. Measuring radii and limb darkening profiles of late-type stars probes the stratification and extension of cool star atmospheres, enables critical tests of three-dimensional stellar atmosphere models, and provides crucial information for the interpretation of high-resolution spectra taken during planetary transits. Tracing the evolution of convection cells in supergiants, following shocks in Mira atmospheres, and Doppler imaging of stellar surfaces are examples of applications that benefit strongly from the combination of spatial and spectral information. Measuring the phase shift between the red and blue wings of photospheric absorption lines provides direct information about the rotation rate and orientation of the rotation axis, an important piece of information on the geometry of stellar binaries and planetary systems with orbits determined by Gaia astrometry. The fringe-tracking stability achieved by Gravity makes it possible to use an instrument requiring long integration times as the science beam combiner, opening the path to using "standard" cross-dispersed echelle spectrographs for this purpose. I will discuss the science drivers for a high-spectral-resolution addition to the VLTI, and present a concept how this could be implemented with modest resources.