Fostering metacognition can be challenging within large enrollment settings, particularly within STEM fields concentrating on problem-solving skills and their underlying theories. Herein, the research problem of realizing more frequent, insightful, and explicitly-rewarded metacognition activities at significant scale is investigated via a strategy utilizing a hierarchy of assessments. Referred to as the "STEM-Optimal Digitized Assessment Strategy (SODAS)," this targeted approach engages frequent assessment, instructor feedback, and learner self-reflection across the hierarchy of learning mechanisms comprising Bloom's Taxonomy of Learning Domains. SODAS spans this hierarchy of learning mechanisms via a progression of (i) unregulated online assessment, (ii) proctored Computer-Based Assessment (CBA), (iii) problem-based learning activities assessed in the laboratory setting, and (iv) personalized Socratic discussions of scanned scrap sheets that accompanied each learner's machine-graded formative assessments. Results of a case study integrating SODAS within a high-enrollment Mechanical Engineering Heat Transfer course at a large state university are presented for enrollment of 118 students. Six question types were delivered with lockdown proctored testing via auto-grading within the Canvas Learning Management System (LMS), along with bi-weekly laboratory activities to address the higher layers of Bloom's Taxonomy. Sample assessment formats were validated through student use and schedules of responsibilities for instructors across four tiers of assessment levels (facts, concepts, procedures, and metacognition), two testing delivery mechanisms (electronic textbook exercises and proctored CBA), and three remediation mechanisms (self-paced, score clarification, and experiment clarification), which showed that learning achievement can increase by up to 16.9% compared to conventional assessment strategies, while utilizing comparable instructor resources and workloads.