For effective human-robot interaction, we argue that robots must gain social-cognitive mechanisms that allow them to function naturally and intuitively during social interactions with humans. However, a lack of consensus on social cognitive processes poses a challenge for how to design such mechanisms for artificial cognitive systems. We discuss a recent integrative perspective of social cognition to provide a systematic theoretical underpinning for computational instantiations of these mechanisms. We highlight several commitments of our approach that we refer to as Engineering Human Social Cognition. We then provide a series of recommendations to facilitate the development of the perceptual, motor, and cognitive architecture for this proposed artificial cognitive system in future work. For each recommendation, we highlight their relation to the discussed social-cognitive mechanisms, provide the rationale for these recommendations and potential benefits, and detail examples of associated computational formalisms that could be leveraged to instantiate our recommendations. Overall, the goal of this paper is to outline an interdisciplinary and multi-theoretic approach to facilitate the design of robots that will one day function, and be perceived, as socially interactive and effective teammates.