Kubernetes is a well-known orchestration and management solution for complex and large-scale service architectures in the Cloud Continuum. While it provides very valuable functions from the operation perspective, the high number of control loops it implements significantly enlarges the already wide space of configuration parameters and policies to consider for management purposes. We argue that optimizing complex Kubernetes deployments considering a multi-cloud and edge computing environment would significantly benefit from a Digital Twin approach, enabling an accurate virtual representation of a Kubernetes application to optimize its deployment and management policies. Towards that goal, this work illustrates the design of KubeTwin, a framework to implement Digital Twins of Kubernetes deployments. Furthermore, we present a validation of KubeTwin in a Multi-access Edge Computing (MEC) scenario, which shows its soundness in reenacting realistic Digital Twins of complex and highly distributed Kubernetes deployments. We believe that KubeTwin can provide useful guidance to the research community working in this field.