2D semiconductors can drive advances in quantum science and technologies. However, they should be free of any contamination; also, the crystallographic ordering and coupling of adjacent layers and their electronic properties should be well-controlled, tunable, and scalable. Here, these challenges are addressed by a new approach, which combines molecular beam epitaxy and in situ band engineering in ultra-high vacuum of semiconducting gallium selenide (GaSe) on graphene. In situ studies by electron diffraction, scanning probe microscopy, and angle-resolved photoelectron spectroscopy reveal that atomically-thin layers of GaSe align in the layer plane with the underlying lattice of graphene. The GaSe/graphene heterostructure, referred to as 2semgraphene, features a centrosymmetric (group symmetry D3d) polymorph of GaSe, a charge dipole at the GaSe/graphene interface, and a band structure tunable by the layer thickness. The newly-developed, scalable 2semgraphene is used in optical sensors that exploit the photoactive GaSe layer and the built-in potential at its interface with the graphene channel. This proof of concept has the potential for further advances and device architectures that exploit 2semgraphene as a functional building block.