The role of "design" in the exploration of integrated "Science, Technology, Engineering, and Mathematics" (STEM) education has rapidly expanded in recent years. "Design" has made an important contribution by providing instructional scaffolds in synthesising knowledge from multiple disciplines to solve real-world problems. Despite the potential of "Design-based Pedagogy" (DBP), there is a paucity of applicable DBP process models for constructing integrated STEM tasks and formulating implementation approaches. To address this issue, we enquire into the "Solution-based Design Process" (SBDP) that reconciles curriculum content knowledge and teaching through authentic problem finding and solving. Through an exploratory study of a self-critical reflection in autoethnographic design practice, we explore how the optimised SBDP can inform (i) The "design skills" and "mindsets" of DBP for "integrated STEM education," and (ii) The "instructional processes" for constructing and implementing integrated STEM tasks involving design models. As found in this study, a unique feature of the Solution-based DBP is that it relates to the processes of thinking and reasoning--highly cognitive and logical; its application requires the skilled operation of 3D printing-based digital fabrication. Additionally, we demonstrated a Solution-based DBP, combined with 3D printing-based digital fabrication, and providing teachers with a structural blueprint for developing integrated STEM programs. Overall, this research contributes to the corpus of methodologically rigorous and evidence-based studies on design-led integrated STEM curriculums in the context of a specific country's education system.