Critical Discourse Studies (CDS) and Food Studies share a number of aims, with CDS increasingly being used as methodological framework in food-related studies. I talk about this in The discursive construction of class and lifestyle (Tominc 2017: 152) where I discuss how CDS is particularly suitable to study food, since food, like CDS, is “’a congenial and fertile base for activist analysis for hunger, inequality, neocolonialism, biotechnology and globalization’ (Belasco 2002: 10), areas also at the core of CDA’s agenda [hence] food research lends itself particularly well to critical perspectives”.
Here is bibliography of works where food intersects with critical discourse studies (not EVERYTHING is here, obviously, but if you know of other such work, please let me know and I will include it):