Phase change memory (PCM) is an emerging data storage technology, however its programming is thermal in nature and typically not energy-efficient. Here we reduce the switching power of PCM through the combined approaches of filamentary contacts and thermal confinement. The filamentary contact is formed through an oxidized TiN layer on the bottom electrode, and thermal confinement is achieved using a monolayer semiconductor interface, three-atom thick MoS2. The former reduces the switching volume of the phase change material and yields a 70% reduction in reset current versus typical 150 nm diameter mushroom cells. The enhanced thermal confinement achieved with the ultra-thin (~6 {AA}) MoS2 yields an additional 30% reduction in switching current and power. We also use detailed simulations to show that further tailoring the electrical and thermal interfaces of such PCM cells toward their fundamental limits could lead up to a six-fold benefit in power efficiency.