A Digital Twin of an Organization (DTO) is a mirrored representation of an organization, aiming to improve the business process of the organization by providing a transparent view over the process and automating management actions to deal with existing and potential risks. Unlike wide applications of digital twins to product design and predictive maintenance, no concrete realizations of DTOs for business process improvement have been studied. In this work, we aim to realize DTOs using action-oriented process mining, a collection of techniques to evaluate violations of constraints and produce the required actions. To this end, we suggest a digital twin interface model as a transparent representation of an organization describing the current state of business processes and possible configurations in underlying information systems. By interacting with the representation, process analysts can elicit constraints and actions that will be continuously monitored and triggered by an action engine to improve business processes. We have implemented a web service to support it and evaluated the feasibility of the proposed approach by conducting a case study using an artificial information system supporting an order handling process.