ABSTRACT Interferometric observations of the mm dust distribution in protoplanetary discs are now showing a ubiquity of annular gap and ring substructures. Their identification and accurate characterization are critical to probing the physical processes responsible. We present frankenstein (frank), an open source code that recovers axisymmetric disc structures at a sub-beam resolution. By fitting the visibilities directly, the model reconstructs a disc’s 1D radial brightness profile non-parametrically using a fast (≲1 min) Gaussian process. The code avoids limitations of current methods that obtain the radial brightness profile either by extracting it from the disc image via non-linear deconvolution at the cost of reduced fit resolution or by assumptions placed on the functional forms of disc structures to fit the visibilities parametrically. We use mock Atacama Large Millimeter Array observations to quantify the method’s intrinsic capability and its performance as a function of baseline-dependent signal-to-noise ratio. Comparing the technique to profile extraction from a clean image, we motivate how our fits accurately recover disc structures at a sub-beam resolution. Demonstrating the model’s utility in fitting real high- and moderate-resolution observations, we conclude by proposing applications to address open questions on protoplanetary disc structure and processes.