Increasingly complex particles are pushing the limits of traditional simulation techniques used to study self-assembly. In this work, we test the use of a learning-augmented Monte Carlo method for predicting low energy configurations of patchy particles shaped like “Tetris®” pieces. We extend this method to compare it against Monte Carlo simulations with cluster moves and introduce a new algorithm—bottom-up building block assembly—for quickly generating ordered configurations of particles with a hierarchy of interaction energies.