We demonstrate the fabrication and characterization of on-chip vertically-emitting SiNx/Au nanopatch cavities containing a monolayer of colloidal quantum dots. The fabrication process is based on electron-beam lithography and deterministically positions both the cavity and the emitters within the cavity with an accuracy of 10 nm. The Purcell enhancement of the spontaneous emission of the quantum dots is studied theoretically and experimentally. The fabrication technique makes it possible to pattern the quantum dot monolayer such that the quantum dots only occupy the center of the nanopatch cavity where a Purcell factor up to 7 can be reached. The work paves the way towards scalable fabrication of bright and directive single-photon sources.