We present a methodology to learn explicit Model Predictive Control (eMPC) laws from sample data points with tunable complexity. The learning process is cast in a special Neural Network setting where the coefficients of two linear layers and a parametric quadratic program (pQP) implicit layer are optimized to fit the training data. Thanks to this formulation, powerful tools from the machine learning community can be exploited to speed up the offline computations through high parallelization. The final controller can be deployed via low-complexity eMPC and the resulting closed-loop system can be certified for stability using existing tools available in the literature. A numerical example on the voltage-current regulation of a multicell DC-DC converter is provided, where the storage and on-line computational demands of the initial controller are drastically reduced with negligible performance impact. Copyright (C) 2020 The Authors.