燉 means stewed and 冬菇 is a type of very delicious Chinese mushroom. This is the name of a dish, but it also describes the act of being demoted at work. This one is pretty interesting. Back in the old days, uniformed policemen in Hong Kong wore a triangular hat that looked like a 冬菇 mushroom.
If a policeman got to a high enough rank, he’d get the benefit of wearing plain clothes, and would no longer need to wear the 冬菇 hat. However, if he got demoted, he could lose his plain clothes privileges and be forced to return to wearing the uniform, including the mushroom hat.
Today people in all professions use this phrase to describe the act of being demoted.