  Brown dwarfs (BDs) possessing masses within the range $40-60 M_{\rm Jup}$ are
rare around solar-type main-sequence (MS) stars, which gives rise to the brown
dwarf desert (BDD). One caveat associated with previous studies of BDD is the
relatively limited sample size of MS$-$BD binaries with accurately determined
BD masses. We aim to produce a large sample of brown dwarf companions with
precisely determined mass around main-sequence A-F-G type stars using
observations of post common-envelope white dwarf (WD)$-$BD binaries. We employ
the rapid binary evolution code COMPAS to deduce the properties of MS$-$BD
binary progenitors from post common-envelope WD$-$BD binaries. This method
supplements the directly observed MS$-$BD binary sample, enriching the data
available for analyzing BDD around main-sequence A-F-G type stars. Our study
opens a new window for studying the shape of BDD around A-F-G type
main-sequence stars in the short period regime. We find tentative evidence that
the `driest' part of BDD around A-F-G type stars may extend into an orbital
period of several hundred days, albeit with a small sample size. More post
common-envelope WD$-$BD binaries detected in the future will advance our
understanding of the BDD around A-F-G type stars.
