The 고 clause attaches whatever accompanies the eating, and 드시다 is the respectful word for 먹다, used about the person being served. These lines are hosts and guests: eating it without adding anything, eating it knowing what is in it, stocking it up and eating it, keeping it at home to eat later, tying your hair back before eating. Trust me and try it appears twice, which is close to a stock food-show line.