We present coordinated multiwavelength observations of the high Galactic latitude (b=+50 • ) black hole X-ray binary (BHXB) Swift J1357.2−0933 in quiescence. Our broadband spectrum includes strictly simultaneous radio and X-ray observations, and near-infrared, optical, and ultraviolet data taken 1-2 days later. We detect Swift J1357.2−0933 at all wavebands except for the radio (f 5GHz <3.9 µJy beam −1 ; 3σ rms ). Given current constraints on the distance (2.3-6.3 kpc), its 0.5-10 keV X-ray flux corresponds to an Eddington ratio L X /L Edd = 4 × 10 −9 − 3 × 10 −8 (assuming a black hole mass of 10M ⊙ ). The broadband spectrum is dominated by synchrotron radiation from a relativistic population of outflowing thermal electrons, which we argue to be a common signature of short-period quiescent BHXBs. Furthermore, we identify the frequency where the synchrotron radiation transitions from optically thick-to-thin (ν b ≈ 2 − 5 × 10 14 Hz, which is the most robust determination of a 'jet break' for a quiescent BHXB to date. Our interpretation relies on the presence of steep curvature in the ultraviolet spectrum, a frequency window made observable by the low amount of interstellar absorption along the line of sight. High Galactic latitude systems like Swift J1357.2−0933 with clean ultraviolet sightlines are crucial for understanding black hole accretion at low luminosities.