This paper introduces DAC-HRC, a novel cognitive architecture designed to optimize human-robot collaboration (HRC) in industrial settings, particularly within the context of Industry 4.0. The architecture is grounded in the Distributed Adaptive Control theory and the principles of joint intentionality and interdependence, which are key to effective HRC. Joint intentionality refers to the shared goals and mutual understanding between a human and a robot, while interdependence emphasizes the reliance on each other’s capabilities to complete tasks. DAC-HRC is applied to a hybrid recycling plant for the disassembly and recycling of Waste Electrical and Electronic Equipment (WEEE) devices. The architecture incorporates several cognitive modules operating at different timescales and abstraction levels, fostering adaptive collaboration that is personalized to each human user. The effectiveness of DAC-HRC is demonstrated through several pilot studies, showcasing functionalities such as turn-taking interaction, personalized error-handling mechanisms, adaptive safety measures, and gesture-based communication. These features enhance human-robot collaboration in the recycling plant by promoting real-time robot adaptation to human needs and preferences. The DAC-HRC architecture aims to contribute to the development of a new HRC paradigm by paving the way for more seamless and efficient collaboration in Industry 4.0 by relying on socially adept cognitive architectures.