This full paper explores project-based learning as a pedagogical tool for cultivating critical thinking and scientific reasoning skills among engineering students. While critical thinking and scientific reasoning are central to the world of engineering, they are often not explicitly taught in conventional engineering curricula. Recent innovations in engineering education have included teaching these essential skills through dedicated courses. However, these new courses rely on traditional lecture-based pedagogy typically used in the humanities, which has proven ineffective for engineering students. Alternative pedagogical approaches, such as peer-to-peer learning and flipped classrooms, provide more engaging and contextualized learning experiences, particularly for skill-based courses. The novel approach which is investigated in this research paper is the use of project-based learning as an effective pedagogy to teach an intensive theoretical course on critical thinking. The course, titled ‘The Art of Thinking and Reasoning’, was designed and taught to 137 first-year students, aiming to instill in them the cognitive skills of critical thinking and scientific reasoning in an engineering context. The course was structured in two parts: the first part employed traditional lecture-driven pedagogy, and the second part utilised a project-based learning approach. Each part included an assessment, the first assessment was a traditional assignment focused on conceptual and reflective thinking through the writing of scripts. It challenged students to envision the future of critical thinking, scientific reasoning, and inquiry, by writing out a 'Future Manifesto'. In contrast, the second assessment required students to compare and revise Bloom's Taxonomy and build a taxonomy of engineering thinking in four stages of a project. Through this exercise, students critiqued existing models and proposed a new taxonomy tailored to engineering problem-solving. This project-based assignment necessitated that students apply their thinking skills in a concrete and hands-on manner, effectively bridging theory and practice. This paper argues that project-based approaches are more effective in embedding critical thinking skills in engineering students by introducing engineering-specific stages that reflect the practical and iterative nature of problem-solving. The practical engagement required by the taxonomy project better mirrors the problem-solving nature of engineering, making it a more suitable method for developing critical and innovative thinking.