The coexistence of robots and humans in shared physical and social spaces is expected to increase. A key enabler of high-quality interaction is a mutual understanding of each other's actions and intentions. In this paper, we motivate and present a systematic user experience (UX) evaluation framework of action and intention recognition between humans and robots from a UX perspective, because there is an identified lack of this kind of evaluation methodology. The evaluation framework is packaged into a methodological approach called ANEMONE (action and intention recognition in human robot interaction). ANEMONE has its foundation in cultural-historical activity theory (AT) as the theoretical lens, the seven stages of action model, and user experience (UX) evaluation methodology, which together are useful in motivating and framing the work presented in this paper. The proposed methodological approach of ANEMONE provides guidance on how to measure, assess, and evaluate the mutual recognition of actions and intentions between humans and robots for investigators of UX evaluation. The paper ends with a discussion, addresses future work, and some concluding remarks.