1. What does it mean?
디저트 배 refers to feeling full after a meal yet still wanting something sweet. People say 디저트 배는 따로 있다, imagining a separate space reserved for dessert.
Also written or said as dijeoteu bae
2. The nuance
It is an everyday food joke, not a claim that humans literally have a second stomach. Someone saying it may simply mean dessert looks appealing.
3. Examples
“배부르다더니 케이크 보고 디저트 배가 생겼대.”
They said they were full, then saw cake and joked that they had room for dessert.
“오늘은 디저트 배도 없어서 다음에 먹으려고 해.”
Today I don't even have room for dessert, so I'll have it another time.
Sources
References support the meaning and usage. Example sentences are written for NoCapWiki.