Numerical Stochastic Perturbation Theory (NSPT) has over the years proved to be a valuable tool, in particular being able to reach unprecedented orders for Lattice Gauge Theories, whose perturbative expansions are notoriously cumbersome. One of the key features of the method is the possibility to expand around non-trivial vacua. While this idea has been around for a while, and it has been implemented in the case of the (non-trivial) background of the Schrödinger functional, NSPT expansions around instantons have not yet been fully worked out. Here we present computations for the double well potential in quantum mechanics. We compute a few orders of the expansion of the ground-state energy splitting in the one-instanton sector. We discuss how (already) known two-loop results are reproduced and present the current status of higher-order computations.