I still suggest that Mr. Krabs hired that nerdy fish from the end of Graveyard Shift as a substitute fry cook.
But we don't know if he was hired or not. He asked for an application, but it was never shown if he actually got the application or not; it does prove, however, that Mr. Krabs was looking for more employees. This suggests that somebody, other than Mr. Krabs and Squidward, cooks the patties when SpongeBob isn't there.
Remember in Plankton's Army when Mr. Krabs pushes Squidward off the register and takes the robot's order? Mr. Krabs shows that he has knowledge of using the register, which means it's not an impossible thought of knowing how to work a grill.
Also, Squidward and SpongeBob are shown going to work at the same time in Funny Pants; this proves that Squidward could not had been working beforehand. This also proves that the restaurant had not been opened before the employees had to get there.
Although these points may be true, I believe that the writers just haven't thought about this. I really think that if they did, they'd go with Mr. Krabs cooking the patties. Although, Mr. Krabs probably wouldn't be doing it in the first place. The only time Mr. Krabs was seen working was in Bummer Vacation, but he was forced to by laws. With this in mind, the restaurant should had been closed and the writers had messed up.