In this work, we propose using differentiable cascaded biquads to model an audio distortion effect. We extend trainable infinite impulse response (IIR) filters to the hyperconditioned case, in which a transformation is learned to directly map external parameters of the distortion effect to its internal filter and gain parameters, along with activations necessary to ensure filter stability. We propose a novel, efficient training scheme of IIR filters by means of a Fourier transform. Our models have significantly fewer parameters and reduced complexity relative to more traditional black-box neural audio effect modeling methodologies using finite impulse response filters. Our smallest, best-performing model adequately models a BOSS MT-2 pedal at 44.1 kHz, using a total of 40 biquads and only 210 parameters. Its model parameters are interpretable, can be related back to the original analog audio circuit, and can even be intuitively altered by machine learning non-specialists after model training. Quantitative and qualitative results illustrate the effectiveness of the proposed method.