As noble liquid time projection chambers grow in size their high voltage requirements increase, and detailed, reproducible studies of dielectric breakdown and the onset of electroluminescence are needed to inform their design. The Xenon Breakdown Apparatus (XeBrA) is a 5-liter cryogenic chamber built to characterize the DC high voltage breakdown behavior of liquid xenon and liquid argon. Electrodes with areas up to 33~cm$^2$ were tested while varying the cathode-anode separation from 1 to 6~mm with a voltage difference up to 75~kV. A power-law relationship between breakdown field and electrode area was observed. The breakdown behavior of liquid argon and liquid xenon within the same experimental apparatus was comparable.