Hexagonal boron nitride (h-BN) adsorbed on metal surfaces shows great promise for applications in nanoscience. Depending on the nature of the substrate, effects such as an extended corrugation of the monolayer can be observed and utilized, e. g. for the patterning of adsorbed molecules. Here we present an in-depth computational study of the structural and electronic properties of a 6 nm Moire pattern formed by a rotated layer of h-BN on a Cu(111) surface. In contrast to related systems, the h-BN layer undergoes only minute structural changes upon adsorption. Nevertheless, the projected density of states at various atoms in the cell and the electrostatic potential above the surface are periodically modulated, leading to the experimentally observed electronic corrugation. We rationalize this observation with the variation in adsorption registry resulting in periodic changes of the lateral, rather than vertical, h-BN-Cu distances.