The increasing environmental impact of Information and Communication Technologies (ICTs), particularly the energy consumption associated with serverless applications, necessitates the development of methodologies to optimize energy efficiency. This study addresses the need for energy-aware design and runtime adaptation in serverless architectures. To develop and validate a methodology that integrates energy monitoring into the development and runtime management of serverless applications, thereby enabling significant reductions in energy consumption while maintaining functionality. A new version of FUSPAQ, a framework for the optimisation of serverless applications, was developed. This version incorporates tools like Kepler for real-time energy monitoring and employs an energy-aware orchestration mechanism to dynamically select energy-efficient function configurations. Validation was conducted through a facial recognition case study and benchmark experiments, comparing energy consumption across different scenarios with and without the proposed adaptations. The enhanced FUSPAQ framework successfully integrated energy consumption metrics into the decision-making process for function selection and runtime adaptation. Benchmark tests confirmed the scalability of the solution, with energy-efficient outcomes even in complex applications. The study highlights the potential of integrating energy-aware practices in serverless applications, presenting a scalable and practical approach to reducing their environmental footprint. By leveraging tools like Kepler and frameworks like FUSPAQ, developers can achieve significant energy savings without compromising application performance. This work contributes to the advancement of Green Software Engineering by emphasizing runtime energy adaptation in Function-as-a-Service (FaaS) architectures. • Energy monitoring integrated into serverless application development. • The approach enables runtime energy-efficient self-adaptation for serverless apps. • Validated using a benchmark application that achieves up to 50% energy savings. • Kepler used for accurate energy metrics in containerized serverless functions. • Demonstrated scalability for optimizing energy across complex FaaS systems.