We present the discovery of 11 new transiting brown dwarfs (BDs) and low-mass M dwarfs from NASA's Transiting Exoplanet Survey Satellite (TESS) mission: TOI-2844, TOI-3122, TOI-3577, TOI-3755, TOI-4462, TOI-4635, TOI-4737, TOI-4759, TOI-5240, TOI-5467, and TOI-5882. They consist of five BD companions and six very-low-mass stellar companions ranging in mass from 25M_J_ to 128M_J_. We used a combination of photometric time-series, spectroscopic, and high-resolution imaging follow-up as a part of the TESS Follow-up Observing Program (or TFOP) to characterize each system. With over 50 transiting BDs confirmed, we now have a large enough sample to directly test different formation and evolutionary scenarios. We provide a renewed perspective on the transiting "brown dwarf desert" and its role in differentiating between planetary and stellar formation mechanisms. Our analysis of the eccentricity distribution for the transiting BD sample does not support previous claims of a transition between planetary and stellar formation at ~42M_J_. We also contribute a first look into the metallicity distribution of transiting companions in the range 7-150M_J_, showing that this does not support a ~42M_J_ transition too. Finally, we also detect a significant lithium absorption feature in one of the BD hosts (TOI-5882). However, we determine that the host star is likely old based on rotation, kinematic, and photometric measurements. We therefore claim that TOI-5882 may be a candidate for planetary engulfment.