Developing techniques for the safe dissipation of the energy carried by Runaway Electrons (REs) in tokamaks is necessary for the operation of future fusion reactors. Evaluating the efficacy of these techniques requires an understanding of the energy transferred to the first wall due to the impact of electrons. The heat flux impinging on the wall in turn depends upon the RE energy distribution prior to the interaction. To gain further insight into these interactions, a dedicated diagnostic for measuring the Hard X-Ray (HXR) radiation emitted from the bremsstrahlung collisions of electrons has been developed, installed and operated on TCV. The design and first results of the Lanthanum Bromide Detector of Runaway Electrons (LaBrDoRE) performed at TCV are presented. The diagnostic was calibrated using its own intrinsic radioactivity and validation of the measurement was demonstrated via comparison with other diagnostics. Measurements made during discharges with REs provide evidence for MHD induced transport of runaways as observed previously on other devices, as well as a reduction in the measured energy in recombined companion plasmas. In order to interpret the measurement, the interaction of MeV electrons with a TCV carbon tile has been modelled using Geant4. A parameter scan was performed to calculate the HXR emission spectrum in terms of the angular and momentum space distribution function of the photons and the energy deposited by the electrons in the tile as a function of the initial energy and impact angles of the electron beams with respect to the tile. This was then used to characterize LaBrDoRE measurements and provide the information necessary to model heat transport within the target tile.