The two main trends in the development of higher education worldwide are universal access and digital transformation. These trends are bringing about an increase in class sizes and the growth of online higher education. Previous studies indicated that both the large-class setting and online delivery threaten the quality, and the exploration of strategies to ensure quality teaching and learning in the large-class setting was in face-to-face or blended learning mode. This study contributes to this topic by exploring the quality of teaching and learning in a new scenario: the fully online large university class. Furthermore, it proposes to use student engagement as a new means to explore the quality of teaching and learning in a large-class setting as it offers evidence on quality from the in-itinere perspective rather than the more commonly ex-post perspective offered by existing studies, collected, for example, from student feedback or course grades. This study was conducted in a mandatory course at an Italian university. Both the Moodle log data and students' reflective diaries are collected to analyze the presence of students' behavioral, emotional, and cognitive engagement. Tableau and NVivo handle the quantitative and qualitative data, respectively. By confirming the presence of all three types of engagement, the result indicates quality teaching and learning happens in the fully online large university class. Since we select both "high-grade" and "low-grade" students as representative samples, the Tableau visualization also indicates that only using behavioral engagement to predict students' academic performance is unreliable.