Engineering instructors play a crucial role in developing a positive culture in their classes. However, few studies have explored integrating teaching pedagogies to convey a culture of care and support students' mental health and well-being (MHWB) in engineering education contexts. It is critical to advance knowledge in this area considering the growing mental health crisis among college students and the engineering education culture considered to be highly rigorous and stressful. Mindfulness training programs have now been widely studied, and scientific research has demonstrated the utility of these programs in supporting MHWB outcomes; however, minimal exploration of their integration in engineering education classrooms has been studied. This paper describes integrating a mindfulness-based intervention (MBI) into an engineering course as a potential advancement in how engineering educators can support student MHWB. We critically evaluated the effects of this MBI in a first-year, project-based engineering course in which 192 students participated in nine mindfulness meditation sessions during the initial 5-10 minutes of class across a 16-week semester term. We used a mixed methods approach with a pre-post survey to assess the impact of the MBI. Quantitative data was collected before and after the interventions to assess potential changes in trait mindfulness and resilience. Qualitative data was collected in the post-survey to gauge students' perceptions of the MBI. Participants who engaged with the mindfulness meditations did not demonstrate a significant improvement in trait mindfulness and resilience. Qualitatively, participants generally reported value in the interventions, noting stress reduction and increased focus. Results suggest most students are supportive of integrating mindfulness meditation into engineering courses. However, there was considerable variation in students' perception of the meditations themselves.