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 , and a radius of R-b = 0.75 0.02 . Its host star, TOI-569, has a mass of M-star = 1.21 0.05, a radius of R-star = 1.47 0.03 dex, and an effective temperature of T-eff = 5768 110 K. TOI-1406b has an orbital period of P = 10.57415 0.00063 days, a mass of M-b = 46.0 2.7 , and a radius of R-b = 0.86 0.03 . The host star for this BD has a mass of M-star = 1.18 0.09 a radius of R-star = 1.35 0.03 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 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.