The origin of Extragalactic Background (EGB) light in the 300 keV - 30 MeV energy range is an unsolved question that has persisted for more than 40 years. MAMBO (Mini Astrophysical MeV Background Observatory) is a CubeSat mission concept motivated by the realization that an instrument purpose-built for measuring the MeV EGB from a CubeSat can provide quality measurements that exceed the best that are currently available. There are two key reasons for this: (1) the EGB is so bright at MeV energies that it only requires an instrument with a small effective area and (2) the best existing measurements are compromised by instrumental background, which scales with the mass of the spacecraft/instrument. Here, small is beautiful. We present a design for a gamma-ray spectrometer capable of both providing quality measurements of the spectrum and angular distribution of the MeV EGB and meeting the tight Size, Weight, and Power (SWaP) constraints imposed by deployment on a 6U CubeSat. During a two year baseline mission, MAMBO will be able to collect measurements of the MeV EGB background that are superior to the best currently available and place important constraints on MeV EGB origin.