As the carbon footprint of the Information and Communication Technology (ICT) sector continues to grow, Sustainability is increasingly recognized as a critical non-functional requirement in software engineering. While existing research predominantly focuses on Green Code, which targets implementation-level optimizations, such micro-level improvements can be undermined by architectural inefficiencies. This vision paper articulates the concept of Green Architectural Reconstruction, advocating a shift from performance-centric code optimization to energy-centric architectural reasoning. To address structural inefficiencies that cannot be resolved at the implementation level, we propose an LLM-driven method to reverse-engineer legacy software architectures and support architectural reasoning about energy-related design trade-offs. Specifically, we explore how AI-assisted architectural distillation can identify architectural energy anti-patterns (e.g., over-provisioned or overly chatty microservices) and inform refactoring decisions toward more sustainable designs. We outline a research roadmap and an experimental framework for architectural energy analysis, providing a conceptual basis for defining architectural energy metrics and guiding future empirical validation. By positioning energy efficiency as a first-class architectural concern, this work contributes a foundation for future research on sustainability-aware software architecture.