The initial-boundary value problem (ibvp) for the nonlinear Schrödinger (NLS) equation on the half-plane with nonzero boundary data is studied by advancing a novel approach recently developed for the well-posedness of the cubic NLS equation on the half-line, which takes advantage of the solution formula produced via the unified transform of Fokas for the associated linear ibvp. For initial data in Sobolev spaces on the half-plane and boundary data in Bourgain spaces arising spontaneously when the linear ibvp is solved with zero initial data, the present work introduces a natural method for proving local well-posedness of nonlinear ibvps in higher dimensions.