Energy-efficient LLM serving requires minimizing serving GPU energy while meeting latency and throughput service-level objectives (SLOs). Attention--FFN disaggregation (AFD) enables separate resource allocation and operating controls for attention and expert computation, but their energy effects remain coupled through the execution pipeline. Realizing its energy-saving potential therefore requires navigating a hierarchical configuration space in which deployment structures constrain admissible controls and shape their end-to-end effects. Finding low-energy configurations that meet SLOs is challenging because physical evaluations are costly and only a small fraction of candidates can be measured. We present Energy-Oriented Configuration Optimization (ECO), which jointly searches deployment structures and their admissible operating controls under a limited measurement budget. ECO constructs a structure-aware energy prior from calibrated stage behavior and pipeline dependencies, then learns residual prediction errors with a Gaussian process. Its cost-aware constrained Bayesian optimization prioritizes measurements according to expected energy improvement while accounting for SLO feasibility, execution success, and evaluation cost, and returns the lowest-energy measured feasible configuration. Across all 16 scenarios on A6000 and A100 with Qwen and DeepSeek, ECO's frozen configurations, evaluated on disjoint requests, reduce serving energy by 40.5\% and increase output token rate by 20.7\% on average relative to baselines while meeting target SLOs. Across the 8 A6000 scenarios, its selected feasible energy averages 33.1\% below generic constrained Bayesian optimization and 25.8\% below genetic search.

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