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In the show 人民的名義 the suspect doesn't want to accompany the protagonist on account of his soup getting cold. The protagonist replies "講究啊"（meticulous！）and then:
原湯化原食
None of my many Pleco dictionaries lists 原湯 or 原食，although 原湯 was my phonetic keyboard's first suggestion!
原汤化原食 is a kind of eating habit, especially exists in northern areas; means drinking the soup of the dumplings (or noodles etc) after eating them. e.g. for the case of dumplings, 原汤 refers to the water (or you can think it as soup) which used for boiling dumplings, 原食 means dumplings.
一般来讲，“原食”指的是淀粉类食物，比如饺子、面条、馄饨、汤圆等，“原汤”就是水煮这些食物后得到的汤，而“化”有“消化”的意思。所以“原汤化原食”的意思是，汤能够帮助淀粉类食物消化吸收。
(In general, 原食 refers to starchy foods, like dumplings, noodles, wontons, glue puddings etc, 原汤 refers to the water which used for boiling these foods. 化 means digestion, so 原汤化原食 means the soup could help digesting starchy foods.)
There're several various explanations about why people doing this, someone believe 原汤 could help digestion; someone believe 原汤 is nourishing. I prefer to that it's just a habit; people like drinking something after eating and with 原汤 you don't need to cook the soup separately. And I think this article gave a nice summary:
所以，真要较真的话，“专家”们提供的“原汤化原食”的“科学道理”实在是很牵强附会。当然，面汤本身并没有什么不好，与白开水相比，它其中还有一些淀粉甚至维生素。吃完面后喝点面汤，多少也算是节约粮食的表现。如果真的喜欢喝，“喜欢”就是最好的理由。如果非要堆砌一些科学术语来给它一个“科学解释”，可能就是弄巧成拙。
