Progress in the semiconductor industry relies on the development of increasingly compact devices consisting of complex geometries made from diverse materials. Precise, label-free, and real-time metrology is needed for the characterization and quality control of such structures in both scientific research and industry. However, optical metrology of 2D sub-wavelength structures with nanometer resolution remains a major challenge. Here, a single-shot and label-free optical metrology approach that determines 2D features of nanostructures, is introduced. Accurate experimental measurements with a random statistical error of 18 nm (λ/27) are demonstrated, while simulations suggest that 6 nm (λ/81) may be possible. This is far beyond the diffraction limit that affects conventional metrology. This metrology employs neural network processing of images of the 2D nano-objects interacting with a phase singularity of the incident topologically structured superoscillatory light. A comparison between conventional and topologically structured illuminations shows that the presence of a singularity with a giant phase gradient substantially improves the retrieval of object information in such an optical metrology. This non-invasive nano-metrology opens a range of application opportunities for smart manufacturing processes, quality control, and advanced materials characterization.