Venthraxus Heterodyne's personal kitchen is the kitchen currently used by the prisoners in Castle Heterodyne (they haven't found the main kitchen yet). While it's under the control of one of the Castle's subsystems, it thinks of itself as simply Castle Heterodyne.
It's properly the personal kitchen of Venthraxus Heterodyne's unnamed favourite chef (but "the Unnamed Chef's personal kitchen" is a terrible article name). This chef went crazy, believing himself to be a reincarnated Borgia, probably Lucrezia Borgia, and began poisoning everything he made. In true Heterodyne style, Venthraxus found this funny, and had a separate kitchen made for him. The chef lived there quite happily until he accidentally ate his own cooking. Venthraxus probably found that hilarious. All the background on the kitchen was provided by the kitchen AI itself, which has a reputation for talking...
The greatest priorities for the kitchen would be the food preparations and cooking conducted within it--so much so it will abort attacks for the sake of preserving a souffle. It was also the very first part of Castle Heterodyne to sample Agatha's blood which, you will likely notice, happens at the far end of the first reference link in this article.