Modern GPU-rich HPC systems are increasingly becoming energy-constrained. Thus, understanding an application's energy consumption becomes essential. Unfortunately, current GPU energy attribution techniques are either inaccurate, inflexible, or outdated. Therefore, we propose Wattchmen, a flexible methodology for measuring, attributing, and predicting GPU energy consumption. We construct a per-instruction energy model using a diverse set of microbenchmarks to systematically quantify the energy consumption of GPU instructions, enabling finer-grain prediction and energy consumption breakdowns for applications. Compared with the state-of-the-art systems like AccelWattch (32%) and Guser (25%), across 16 popular GPGPU, graph analytics, HPC, and ML workloads, Wattchmen reduces the mean absolute percent error (MAPE) to 14% on V100 GPUs. Furthermore, we show that Wattchmen provides similar MAPEs for water-cooled V100s (15%) and extends to later architectures, including air-cooled A100 (11%) and H100 (12%) GPUs. Finally, to further demonstrate Wattchmen's value, we apply it to applications such as Backprop and QMCPACK, where Wattchmen's insights enable energy reductions of up to 35%.