Advancements in Cyber-Physical Systems, IoT, Data-driven methods, and networking prepare the adequate infrastructure for constructing new organizations, where everything is connected and interact with each other. A Digital Twin of the Organization (DTO) exploits these infrastructures to provide an accurate digital representation of the organization. Beyond the usual representation of devices, machines and physical assets supplied by Digital Twins, a DTO also include processes, services, people, roles, and all other relevant elements for the operation of organizations. Therefore, DTO can play a key role in realizing and analyzing aspects of organizations, assisting managers on the knowledge of the organization status, and foreseeing possible effects of potential changes in the organization. However, due to the dynamic, open, and ever-changing environment of organizations, an established DTO will soon degrade or even lose all its utility. Therefore, a DTO needs to evolve to recover its utility when the organization changes. The development of flexible, resilient, and easy to evolve DTO has not been well-addressed yet. Most of the existing proposals are context-dependent, system-specific, or focus on providing solutions in high-level abstraction. This work leverages Enterprise Architecture to propose an architectural pattern to serve as a blueprint toward the development of resilient DTO.