Abstract: We investigate the merits of a measurement of the permanent electric dipole moment of the electron (eEDM) with barium monofluoride molecules, thereby searching for phenomena of CP violation beyond those incorporated in the standard model (SM) of particle physics. Although the BaF molecule has a smaller enhancement factor in terms of the effective electric field than other molecules used in current studies (YbF, ThO and ThF+), we show that a competitive measurement is possible by combining Stark-deceleration, laser-cooling and an intense primary cold source of BaF molecules. With the long coherent interaction times obtainable in a cold beam of BaF, a sensitivity of 5 × 10−30 e⋅cm for an eEDM is feasible. We describe the rationale, the challenges and the experimental methods envisioned to achieve this target. Graphical abstract: [Figure not available: see fulltext.].