Coughing after eating is normally due to the build up and overproduction of phlegm. This tends to happen if you have consumed dairy products like cheese, milk, yogurt, or a cream based sauce like Alfredo.
Coughing is often a mild symptom of an allergy. Something in the food you're eating maybe seen as an irritant or allergen by your body, and that's where the phlegm production is coming from- your body produces it as a means of capturing the offending parts and expelling them.
Just be careful. Food allergies get progressively worse over time and with repeated exposure. If your coughing ever goes into even a mild feeling of difficulty breathing you need to get to a doctor.