朵颐 is almost always seen in the four-character phrase
大快朵颐 - 'to eat heartily and with great enjoyment'. Rarely used outside that idiom. The image:
朵 (move / hang down) +
颐 (cheeks) - i.e. cheeks bulging and moving as you chew with pleasure. Origins trace back to
《周易·颐卦》.