Controlling the electronic properties of interfaces has enormous scientific and technological implications and has been recently extended from semiconductors to complex oxides that host emergent ground states not present in the parent materials(1-5). These oxide interfaces present a fundamentally new opportunity where, instead of conventional bandgap engineering, the electronic and magnetic properties can be optimized by engineering quantum many-body interactions(5-7). We use an integrated oxide molecular-beam epitaxy and angle-resolved photoemission spectroscopy system to synthesize and investigate the electronic structure of superlattices of the Mott insulator LaMnO3 and the band insulator SrMnO3. By digitally varying the separation between interfaces in (LaMnO3)(2n)/(SrMnO3)(n) superlattices with atomic-layer precision, we demonstrate that quantum many-body interactions are enhanced, driving the electronic states from a ferromagnetic polaronic metal to a pseudogapped insulating ground state. This work demonstrates how many-body interactions can be engineered at correlated oxide interfaces, an important prerequisite to exploiting such effects in novel electronics.