We report the discovery of two intermediate-mass transiting brown dwarfs (BDs), TOI-569b and TOI-1406b, from NASA's Transiting Exoplanet Survey Satellite mission. TOI-569b has an orbital period of P=.55604±0.00016 days, a mass of Mb = 64.1±1.9 MJ, and a radius of Rb = 0.75±0.02 RJ. Its host star, TOI-569, has a mass of Må = 1.21±0.05 M, a radius of Rå = 1.47±0.03 R, [Fe H 0.29 0.09] = + dex, and an effective temperature of Teff = 5768±10K. TOI-1406b has an orbital period of P=10.57415±0.00063 days, a mass of Mb = 46.0± 2.7 MJ, and a radius of Rb = 0.86±0.03 RJ. The host star for this BD has a mass of Må = 1.18±0.09 M, a radius of Rå = 1.35±0.03 R, [Fe/H] =-0.08± 0.09 dex, and an effective temperature of Teff = 6290±100 K. Both BDs are in circular orbits around their host stars and are older than 3 Gyr based on stellar isochrone models of the stars. TOI-569 is one of two slightly evolved stars known to host a transiting BD (the other being KOI-415). TOI-1406b is one of three known transiting BDs to occupy the mass range of 40-50 MJ and one of two to have a circular orbit at a period near 10 days (with the first being KOI-205b). Both BDs have reliable ages from stellar isochrones, in addition to their well-constrained masses and radii, making them particularly valuable as tests for substellar isochrones in the BD mass-radius diagram.