Challenge-based teaching facilitates students' simultaneous development of content mastery and strategies for applying technical knowledge innovatively. The University of Texas at Austin Department of Biomedical Engineering has offered a challenge-based course on biotransport as an accelerated study-abroad learning experience in Cambridge, England. We used a mixed methods approach to characterize students' learning trajectory, to include technical prowess, problem-solving self-efficacy, and engineering identity throughout the entirety of this course. Students developed problem solving strategies and confidence over the semester and readily transferred their acquired solution framework to technical domains outside of the course subject of biotransport. Students identified challenge-based pedagogies as their preferred methods of classroom instruction, became familiar with corresponding assessments, and identified strongly as practitioners within the engineering field. We believe this illustrative case study provides significant evidence for the effectiveness of challenge-based instruction and can serve as a model for pedagogy-sensitive classroom assessment in engineering.