Brown dwarfs bridge the gap between stars and planets, providing valuable insight into both planetary and stellar-formation mechanisms. Yet the census of transiting brown-dwarf companions, in particular around M-dwarf stars, remains incomplete. We report the discovery of two transiting brown dwarfs around low-mass hosts using a combination of space- and ground-based photometry along with near-infrared radial velocities. We characterize TOI-5389Ab (68.0_-2.2_^+2.2^M_J_) and TOI-5610b (40.4_-1.0_^+1.0^M_J_), two moderately massive brown dwarfs orbiting early M-dwarf hosts (Teff=3569+/-59K and 3618+/-59K, respectively). For TOI-5389Ab, the best fitting parameters are period P=10.40046+/-0.00002d, radius R_BD_=0.824_-0.031_^+0.033^R_J_, and low eccentricity e=0.0962_-0.0046_^+0.0027^. In particular, this constitutes one of the most extreme substellar-stellar companion-to-host mass ratios of q=0.150. For TOI-5610b, the best-fitting parameters are period P=7.95346+/-0.00002d, radius R_BD_=0.887_-0.031_^+0.031^R_J_, and moderate eccentricity e=0.354_-0.012_^+0.011^. Both targets are expected to have shallow, but potentially observable, occultations: <=500ppm in the Johnson K band. A statistical analysis of M-dwarf/BD systems reveals for the first time that those at short orbital periods (P<13d) exhibit a dearth of 13M_J_