We report the discovery of an intermediate-mass transiting brown dwarf, TOI-503b, from the TESS mission. TOI-503b is the first brown dwarf discovered by TESS and orbits a metallic-line A-type star with a period of \(P=3.6772 \pm 0.0001\) days. The light curve from TESS indicates that TOI-503b transits its host star in a grazing manner, which limits the precision with which we measure the brown dwarf's radius (\(R_b = 1.34^{+0.26}_{-0.15} R_J\)). We obtained high-resolution spectroscopic observations with the FIES, Ondřejov, PARAS, Tautenburg, and TRES spectrographs and measured the mass of TOI-503b to be \(M_b = 53.7 \pm 1.2 M_J\). The host star has a mass of \(M_\star = 1.80 \pm 0.06 M_\odot\), a radius of \(R_\star = 1.70 \pm 0.05 R_\odot\), an effective temperature of \(T_{\rm eff} = 7650 \pm 160\)K, and a relatively high metallicity of \(0.61\pm 0.07\) dex. We used stellar isochrones to derive the age of the system to be \(\sim\)180 Myr, which places its age between that of RIK 72b (a \(\sim\)10 Myr old brown dwarf in the Upper Scorpius stellar association) and AD 3116b (a \(\sim\)600 Myr old brown dwarf in the Praesepe cluster). We argue that this brown dwarf formed in-situ, based on the young age of the system and the long circularization timescale for this brown dwarf around its host star. TOI-503b joins a growing number of known short-period, intermediate-mass brown dwarfs orbiting main sequence stars, and is the second such brown dwarf known to transit an A star, after HATS-70b. With the growth in the population in this regime, the driest region in the brown dwarf desert (\(35-55 M_J \sin{i}\)) is reforesting and its mass range shrinking.