This article investigates a control system within the context of sixth-generation wireless networks. The remote control performance optimization confronts the technical challenges that arise from the intricate interactions between communication and control sub-systems, asking for a co-design. Considering the system dynamics, we formulate the sequential co-design decision-makings of communication and control over a discrete time horizon as a Markov decision process, for which a practical offline learning framework is proposed. Our proposed framework integrates large language models into the elements of reinforcement learning. We present a case study on the age of semantics-aware communication and control co-design to showcase the potential of our proposed learning framework. Furthermore, we discuss the open issues remaining to make our offline learning framework feasible for real-world implementations and highlight the research directions for future explorations.