The Adventure of the Clapham Cook by Agatha Christie

Poirot is not interested in investigating some of the cases which appear in the newspapers when Hastings tries to bring them to his attention. These include ones about a bank clerk, Mr. Davis, who disappears with fifty thousand pounds of securities, a suicidal man, and a missing typist. He is put on the spot though when visited by a Mrs. Todd who is determined that he investigate her missing cook. Challenged, he decides, with some humour and to avoid an argument, to take the seemingly trivial case. Eliza Dunn, a middle-aged woman, walked out of her job and the Todd's house in Clapham two days ago without working her notice. She has not communicated with her employer since, except for sending for her trunk that very day. What can Poirot make of this?

The Adventure of the Clapham Cook by Agatha Christie

They want Hercule Poirot to find their cook.  He refuses, but then agrees.

This is a short story but it has plenty of twists and turns.  Hercule uses his grey matter to solve the mystery.  Hastings has an idea but it is fiction.

One of the missing is dead.  The cook Hercule finds and get her story.

Soon he has solved the mystery...