We investigate the optical response of graphene nanoribbons (GNRs) using the broadband nonlinear generation and detection capabilities of nanoscale junctions created at the LaAlO$_3$/SrTiO$_3$ interface. GNR nanoclusters measured to be as small as 1-2 GNRs in size are deposited on the LaAlO$_3$ surface with an atomic force microscope tip. Time-resolved nonlinear optical probes of GNR nanoclusters reveal a strong, gate-tunable second and third harmonic response, as well as strong extinction of visible to near-infrared (VIS-NIR) light at distinct wavelengths, similar to previous reports with graphene.