One of my favorite classic stories is the The Epic of Gilgamesh. Even though the story is the oldest known written text it is not very often that it is retold or referenced in modern story telling. But it seems that the Quays once again wanted to stand out of the crowd by creating a short animated film based on this classic story. However, for the life of me I cannot make the connection between the text and the Quay film "This Unnameable Little Broom (Epic of Gilgamesh)".
For those who have not read it the story is about a king, Gilgamesh, who befriends a man who is somewhat like a beast. Both are supposed to have strength beyond normal men. They go on a few fantastical adventures until Gilgamesh's friend is killed in a battle. Gilgamesh is beside himself with grief for he became so close they we as if lovers. But Gilgamesh is also reminded of his own mortality and sets off to find immortality. However, his travel is in vain and is told that the only way for a man to gain immortality is in his actions as they are retold through out history.
The Quay film, on the other hand, is about a character (who seems to represent a boy) who takes joy in torturing helpless and unsuspecting victims. At one point the film cuts away to an other worldly realm (possibly a post-death state) where life continues to decay.
Possibly its the relation to mortality that connects these two pieces, but I recommend watching the film for yourself and making your own judgements.