  GQ Lup B is a forming brown dwarf companion ($M\sim10-30~M_J$) showing
evidence for an infrared excess associated with a disk surronding the companion
itself. Here we present mid-infrared (MIR) observations of GQ Lup B with the
Medium Resolution Spectrograph (MRS) on JWST, spanning $4.8-11.7~\mu$m. We
remove the stellar contamination using reference differential imaging based on
principal component analysis (PCA), demonstrating that the MRS can perform
high-contrast science. Our observations provide a sensitive probe of the disk
surrounding GQ Lup B. We find no sign of a silicate feature, similar to other
disk surrounding very low mass objects, which likely implies significant grain
growth ($a_{\mathrm{min}}\gtrsim5~\mu$m), and potentially dust settling.
Additionally, we find that if the emission is dominated by an inner wall, the
disk around the companion might have an inner cavity larger than the one set by
sublimation. Conversely, if our data probe the emission from a thin flat disk,
we find the disk to be very compact. More observations are required to confirm
this finding and assess the vertical structure of the disk. This approach paves
the path to the future study of circumplanetary disks and their physical
properties. Our results demonstrate that MIR spectroscopic observations can
reveal the physical characteristics of disks around forming companions,
providing unique insights into the formation of giant planets, brown dwarfs and
their satellites.
