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=6.55604±0.00016 days, a mass of M b = 64.1±1.9 M J , and a radius of R b = 0.75±0.02 R J. Its host star, TOI-569, has a mass of M å = 1.21±0.05 M , a radius of R å = 1.47±0.03 R , = + Fe H 0.29 0.09 [ ] dex, and an effective temperature of T eff = 5768±110K. TOI-1406b has an orbital period of P=10.57415±0.00063 days, a mass of M b = 46.0± 2.7 M J , and a radius of R b = 0.86±0.03 R J. The host star for this BD has a mass of M å = 1.18±0.09 M , a radius of R å = 1.35±0.03 R , =- Fe H 0.08 0.09 [ ] dex, and an effective temperature of T eff = 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 M J 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.