Intersectionality theory examines how matrices of power and interlocking structures of oppression shape and influence people's multiple identities. It reminds us that people's lives cannot be explained by taking into account single categories, such as gender, race, sexuality, or socio-economic status. Rather, human lives are multi-dimensional and complex, and people's lived realities are shaped by different factors and social dynamics operating together. Therefore, when someone occupies multiple marginalized intersections, their individual-level experiences reflect social and structural systems of power, privilege, and inequality. And yet, knowing that people occupy different social locations that afford them unique experiences is not the same as knowing how to analyze data in an intersectional way. Intersectional analyses are rigorous, and require the use of theory at multiple levels to see theoretical connections that are often only implicit. In this paper, we ask "How does one actually do intersectional research and what role does theory play in this process?" In an effort to make intersectionality theory more accessible to health professions education research, this article describes the simpler version of intersectional analyses followed by the more complex version representing how it was originally intended to be used; a means to fight for social justice. Using pilot data collected on first-generation medical students' professional identity experiences, we demonstrate the thinking and engagement with theory that would be needed to do an intersectional analysis. Along the way, we describe some of the challenges researchers may find in using intersectionality in their own work. By re-situating the theory within its original roots of Black feminist thought, we hope other health professions education (HPE) researchers consider using intersectionality in their own analyses.