We present measurements of momentum-resolved magneto-tunneling from a perpendicular two-dimensional (2D) contact into integer quantum Hall (QH) edges at a sharp-edge potential created by cleaved-edge overgrowth. Resonances in the tunnel conductance correspond to coincidences of electronic states of the QH edge and the 2D contact in energy–momentum space. With this dispersion relation reflecting the potential distribution at the edge we can directly measure the band bending at our cleaved edge under the influence of an external voltage bias. At finite bias we observe significant deviations from the flat-band condition in agreement with self-consistent calculations of the edge potential.