In the Girl Genius context, "the Chef", otherwise unqualified, refers specifically to the older one-eyed guy who does the cooking for Master Payne's Circus of Adventure. Curiously, like Balthazar's dad, he's never named in the comic even as he plays a fairly important role in the Circus and the events surrounding it. (He is named Taki in the second novel, and is described as having a Greek accent.) He is first seen , as Agatha and Krosp are bringing the formerly lost Balthazar back to camp.
Like many of the Circus people, he's a minor Spark, and uses his kitchen as his laboratory. His most notable invention is the Calming Pie. The first time we see this remarkable preparation (on Lars), it doesn't work very well, although that might be because Lars is sufficiently rattled that nothing is going to calm him except having Agatha nearby wielding a death ray. The Chef thinks it may be because all the calm has leaked out of the pie (which probably tells you a lot about the way he thinks); nevertheless, he evidently continues to tinker with the formula, and at later juncture . Consequently, he feels much the same triumph that any good chef feels on creating a culinary masterpiece. This is a sobering thought.
Much of his pie making, however, isn't for therapeutic — much less gastronomic — purposes, but rather for ballistic use in the Heterodyne shows. Experience has that "none of the Heterodyne plays really suffer if Punch and Judy start throwing pies." The Chef views this as "another success for my unified pie theory," but more practically, he makes sure there are lots of pies to be thrown. of pies.
Like most of the cohort, he acts in the plays as well, frequently playing a comedic version of Baron Klaus Wulfenbach, wearing a deliberately sloppy wig that conceals his eye-patch. That this actor plays this character is a pretty good sign that the Heterodyne plays don't treat Klaus as a particularly ... heroic ... figure. That said, it should be noted that he asserts that Klaus's character must strive to attempt to maintain his dignity, despite the slapstick, in contrast to, for instance, Punch's character.
Presumably he has decamped to England along with the rest of the Circus.
Completely irrelevant trivia Edit
He never says "hello there children"; that would be another chef entirely.
"Take that, Brillat-Savarin!" is a reference to real world Jean Anthelme Brillat-Savarin (1755 – 1826), a French politician and lawyer best known for his Physiologie du goût (The Physiology of Taste), published in 1825.