• A new concept and framework of the Resilient Cognitive Twin (RCT). • A new generative approach with three enabling mechanisms. • An evaluation case study of a city flooding resilience system. Improving the resilience of an engineering system can be addressed from both a physical engineered system (PES) and its virtual replica--digital twin (DT) system. On the one hand, a DT can enhance the resilience of its PES by enabling real-time monitoring/proactive intervention and predictive maintenance. On the other hand, its deep integration with PES also increases the complexity of the overall system--both virtual and physical. This interdependence can transform single-sided risks into overall system-wide vulnerabilities, potentially undermining--even compromising--the resilience of the PES itself. To address this challenge, this paper proposes a new concept and framework of the Resilient Cognitive Twin (RCT), that supports generative reconfiguration and bidirectional feedback across the human–cyber–physical continuum. The framework is supported by a generative approach with three new enabling mechanisms: (1) a requirement decomposition and recompositing mechanism with edge-cloud-centre collaboration for forming a unified yet loosely coupled and low-level foundation of RCT; (2) a dynamic evolution mechanism enabling right-time co-evolution of data-model-service relationships for a changing environment and stakeholder needs; and (3) a generative cognitive mechanism for situational awareness and decision-making, responding to changing situations with proper and resilient services and their coordination/scheduling. The proposed framework and enabling approach are validated through an urban flood resilient DT system, demonstrating its capability to enhance resilience in complex, distributed environments, paving the way for Human-Cyber-Physical Systems and future industrial and societal applications.