What causes a productive cough after eating? For the past few days, about 10 minutes after every meal, I cough up a large amount of phlegm from lungs

Acid reflux. Acid reflux, also known as gerd, which is very prevalent in overweight people especially (with 60% of americans being overweight, of course). Constant acid coming up from the stomach causes irritation that induces the formation of mucous, constantly trying to clear by coughing. Reflux is increased with smoking. See doctor for management of condition.