Slang for eating a chick's pussy. Another way of saying "going down town" on a woman who wants her clitoris and labia minora given oral stimulus to bring her to orgasm. Can apply to either a man or another woman performing cunnilingus to the recipient woman.
Mike: "I can't stand it! I wanna' give Irene the South Town Face Plant, like right now!"
Tom: "Easy man, take her to dinner first, then have you some dinner."