Ultrathin films of boron nitride (BN) have recently attracted considerable interest given their successful incorporation in graphene nanodevices and their use as spacer layers to electronically decouple and order functional adsorbates. Here, we introduce a BN monolayer grown by chemical vapor deposition of borazine on a single crystal Cu support, representing a model system for an electronically patterned but topographically smooth substrate. Scanning tunneling microscopy and spectroscopy experiments evidence a weak bonding of the single BN sheet to Cu, preserving the insulating character of bulk hexagonal boron nitride, combined with a periodic lateral variation of the local work function and the surface potential. Complementary density functional theory calculations reveal a varying registry of the BN relative to the Cu lattice as origin of this electronic Moiré-like superstructure.