Functions as a Service has emerged as a popular abstraction for a wide range of cloud applications and an important cloud workload. We present the design and implementation of FaasMeter, a FaaS control plane which provides energy monitoring, accounting, control, and pricing as first-class operations. The highly diverse and dynamic workloads of FaaS create additional complexity to measuring and controlling energy usage which FaasMeter can mitigate. We develop a new statistical energy disaggregation approach to provide accurate and complete energy footprints for functions, despite using noisy and coarse-grained system-level power (not just CPU power readings). Our accurate and robust footprints are achieved by combining conventional power models with Kalman filters and Shapley values. FaasMeter is a full-spectrum energy profiler, and fairly attributes energy of shared resources to functions (such as energy used by the control plane itself). We develop new energy profiling validation metrics, and show that FaasMeter's energy footprints are accurate to within 1\% of carefully obtained marginal energy ground truth measurements.