Here are some I recommend.
- 나무 없는 산 (Treeless Mountain, 2008) - quietly moving, close look at two helpless small girls growing up.
- 여행자 (A Brand New Life, 2009) - another one about a child struggling to find her place in life.
- 싱글 라이더 (Single Rider, 2017) - a slow paced movie which follows a man's final journey to the other world.
- 미씽, 사라진 여자 (Missing, 2016) - a thriller and a very sad social commentary at the same time.
- 베테랑 (Veteran, 2015) - a fantastic, well made and action filled cop movie.
The slow ones are the real gems, depicting people like in real life. They may also help you a little with learning Korean.