Engineering education has long resulted in professional engineers with the required technical skills to meet the profession's needs. Yet in today's rapidly changing, globalised world, engineers will need more than technical competencies to meet the requirements of their professional work. Incorporating different literacies in engineering education might help with this shift. We introduce the idea of including critical reflective writing practice on the idea of being an engineer into engineering curricula. Our study explored how fourteen engineering graduate students were mentored on how to reflect critically on their professional identities through narrative writing. The students wrote the narratives while attending a pilot co-curricular Institute that focused on developing leadership, communication, and professional skill-building. We analysed the narrative writing produced by participants using the constant comparison method of analysis. Key findings show that: (1) narrative methodologies are valuable for tapping into the reflective non-technical, process aspects of the profession; and (2) critical reflective writing practice was challenging for participants and required comprehensive scaffolding. If scaffolded and embedded in engineering curricula, critical reflective writing practice could contribute significantly to a 21st century engineering identity.