Missed a large part of the show as I thought Central was showing it another day when I saw the stills of "The Way Home" in the newspaper. In actual fact, the two Korean films were showing on the same 9pm time slot: the former on Central and the latter on Channel U. Incidentally, I was browsing http://us.imdb.com and found that both films are by the same director!
AMBTZ looked quite interesting from the few scenes that I saw! The male and female leads collaborated to write a story that talks about how a girl working at the art museum met a vet at the zoo. Didn't quite catch the details as I was watching "The Apprentice" at the same time but the leads do have the right chemistry together! The female lead, Shim Eun-Ha also acted in "Christmas In August" that is another film that I enjoyed.
Art Museum By the Zoo: IMDB Link
Art Museum By The Zoo: Korean Film Review
Christmas In August: IMDB Link
Christmas In August: Korean Film Review