Quantitative characterization of intrinsic and artificial defects in ferromagnetic structures is critical to future magnetic storage based on vortices or domain walls moving through nanostructured devices. Using torsional magnetometry, we observe finite size modifications to the Barkhausen effect in the limiting case of a single vortex core interacting with individual pointlike pinning sites in a magnetic thin film. The Barkhausen effect in this limit becomes a quantitative two-dimensional nanoscale probe of local energetics in the film. Tailoring the pinning potential using single-point focused ion beam implantation demonstrates control of the effect and points the way to integrated magneto-mechanical devices incorporating quantum pinning effects.