Dorokei (2018)

In a society in which justice is awfully subjective, and the possibility of finding the truth is so complicated, detective Yugami simply chases after the facts of various cases. He will casually approach potential suspects and talk to them in order to attain new information. All he is looking for are the facts. He feels that there is no point in following the rules, nor trying to read the atmospheres of the environment he's in. For him, resorting to unique and illegal investigations is not out of the ordinary. To assist him, he also has a sidekick, Torao Hanyu, who's a serious detective with a completely different personality. For Yugami, he simply wants to arrest as many criminals as possible through his illegal investigation style, so Torao's existence becomes a bother for him. Two detectives with absolutely nothing in common, somehow try to combine their skills in order to combat the enemies of society.

So far it is similar because they both involve the police department and they have a funny duo who work together in a sort of forced way.

The two main characters in both the dramas represent two opposite sides of justice: one is who in the right and other who is in the wrong. In Talio, the two characters work together while in Dorokei its kind of friendship.

Dorokei does not have family-like connection as K2, but it had many similar elements.
1. Detective-crime based story
2. Both have comedic elements
3. Has some revenge based flashback
4. Naive main male leads / new to the job
5. Bromance
6. Corrupted higher officials
I would definitely recommend giving this a try!