Toaru Majutsu no Index-tan Movie: Endymion no Kiseki - Ga Attari Nakattari

Both are a compilation of animated specials that provides a secondary, more humorous perspective on their respective parent story. Both are relatively short in length and should be watched after watching their parent story. Furthermore, Henneko BBS and the Endymion special are both made and released by J.C. Staff, so the artwork and the quality have a lot of matching parallels. 

Both works (in the case of FMA: Premium Collection, only the second episode) features the characters of the series parodying some of the events of their respective movies.