In this paper, we outline research observations concerning EFL teaching research at the university level through the theoretical lens of the cognitive approach. We show how an integrated cognitive and communicative teaching model can help resolve linguistic and content knowledge gaps, identified in the recent survey of non-linguistic students. Then, we present an illustrative case study from Tomsk State University, which suggests a teaching model with the focus on the development of cognitive and communicative skills in learners. Finally, we offer some recommendations for future research at the intersection of cognitive linguistics and pedagogy.