In the context of the intensely debated topic of the impact of entrepreneurship education on students’ entrepreneurial intentions, the current paper presents findings of the entrepreneurial intentions of a group of doctoral students and postdoctoral researchers from different fields of study enrolled in the SmartDoct project—an entrepreneurship education project co-financed through the European Social Fund and implemented by the University of Oradea, Romania, between 2019 and 2022. Our paper investigates individual-level determinants of the intention to become an entrepreneur, grounding in the social-cognitive, planned behaviour, and human capital theories. Using content analysis of semi-structured interviews, the paper offers insights into the narratives related to the entrepreneurial intentions of doctoral and postdoctoral researchers, including relevant suggestions regarding the impact of gender, field of study, perceived influence of behavioural control, social norms concerning social support, and of the role models. Our results document the capacity of entrepreneurial programmes to encourage business initiation via stimulating entrepreneurial self-efficacy, the importance of perceived behavioural control on explaining entrepreneurial intention, and the value of social support and of role models, as well as the salience of the gender and field of study in explaining the net effect of entrepreneurial training in the case of students enrolled in advanced research programmes.