We show theoretically and computationally that solid-state thermionic devices made out of 2D van der Waals layers could have efficiencies as high as thermoelectric modules. Here, we present experimental results for cross-plane thermoelectric transport in gold-graphene-few layers of WSe2-graphene-gold structures. We present a new measurement technique to extract equivalent device figure of merit in a wide temperature range. A small ZT was estimated at room temperatures using cooling curve measurements. It is noted that despite the small value of ZT (0.002), it is orders of magnitude larger than previously reported ZTs for van der Waals heterostructures. It is also noted that higher ZT values are expected at elevated temperatures and better performances are expected when the substrate is replaced by a good heat sink. We discuss design strategies to improve the efficiency and lay the pathway toward highly efficient thermionic devices.