Two-dimensional (2D) nanostructures and nanomaterials offer potential for a wide range of technological applications in electronics, optoelectronics, data storage, sensing and catalysis. On-surface molecular self-assembly – where organic molecules act as building blocks and where surfaces play the role of supporting templates – allows for the bottom-up synthesis of such 2D systems with tuneable atomically precise morphologies and tailored electronic properties. These self-assembly protocols are well established on metal surfaces, but remain limited on electronically gapped substrates (insulators, semiconductors). The latter are useful for preventing electronic coupling (that is, hybridization between molecular assembly and underlying surface) and for avoiding quenching of optical processes, necessary for prospective electronic and optoelectronic applications. In particular, molecular self-assembly on surfaces other than weakly interacting metals can be challenging due to substrate reactivity, defects and inhomogeneities, resulting in intricate energy landscapes that limit the growth kinetically and hampers the synthesis of large-area defect-free 2D systems. Here, we demonstrate the self-assembly of a 2D, atomically thin organic molecular film on a model wide bandgap 2D insulator, single-layer hexagonal boron nitride (hBN) on Cu(111). The molecular film consists of flat, aromatic 9,10-di-cyano-anthracene (DCA) molecules. Our low-temperature scanning tunnelling microscopy and spectroscopy measurements revealed mesoscopic (> 100 x 100 nm^2), topographically homogeneous crystalline molecular domains resulting from flat molecular adsorption and noncovalent in-plane cyano-ring bonding, with electronically decoupled molecular orbitals (MOs) lying within the hBN electronic gap. These MOs exhibit an energy level spatial modulation (~300 meV) that follows the moiré work function variation of hBN on Cu(111). This work paves the way for large-area, atomically precise, highly crystalline 2D organic (and metal-organic) nanomaterials on electronically functional wide bandgap insulators.