This study presents the development of the PsyCogMetrics AI Lab (psycogmetrics.ai), an integrated, cloud-based platform that operationalizes psychometric and cognitive-science methodologies for Large Language Model (LLM) evaluation. Framed as a three-cycle Action Design Science study, the Relevance Cycle identifies key limitations in current evaluation methods and unfulfilled stakeholder needs. The Rigor Cycle draws on kernel theories such as Popperian falsifiability, Classical Test Theory, and Cognitive Load Theory to derive deductive design objectives. The Design Cycle operationalizes these objectives through nested Build-Intervene-Evaluate loops. The study contributes a novel IT artifact, a validated design for LLM evaluation, benefiting research at the intersection of AI, psychology, cognitive science, and the social and behavioral sciences.