A short comedy OVA (straight to DVD/Blu-Ray animation) made for the 10th anniversary of Type-Moon in 2011. It's a cross-over of Fate/Stay Night and Tsukihime that has them act out various comedy sketches that often parody the source material.
Due to its status as a non-canon parody, its hard to get too into the premise without just repeating jokes or describing some of the sketches, so I'd give it a look yourself - each episode is only around 15 minutes.
It lasted approximately 12 episodes with three specials.
Said specials were a playthrough of the Illya's Castle game from hollow ataraxia, an extended episode starring the hollow ataraxia cast and another extended episode featuring Hibiki and Chikagi.
While not using the Carnival Phantasm branding, a mock-up trailer for Fate/Prototype (an adaptation of the original draft for Fate/Stay Night) was animated by the same studio and the final minutes of the last episode of Carnival proper leads into it.