A lot of technological advances depend on next-generation materials, such as graphene, which enables better electronics, to name but one example. Manufacturing such materials is often difficult, in particular, producing graphene at scale is an open problem. We apply state-of-the-art machine learning to optimize the production of laser-induced graphene, an established manufacturing method that has shown great promise. We demonstrate improvements over previous results in terms of the quality of the produced graphene from a variety of different precursor materials. We use Bayesian model-based optimization to quickly improve outcomes based on little initial data and show the robustness of our approach to different experimental conditions, tackling a small-data problem in contrast to the more common big-data applications of machine learning. We analyze the learned surrogate models with respect to the quality of their predictions and learned relationships that may be of interest to domain experts and improve our understanding of the processes governing laser-induced graphene production.