Life on Mars (2018)

Similar Psychopath killer vibes
Psychological thriller
Suspense at every episode which keeps us on the edge of what will happen next
Both ML gets their Brain Damage while catching the killer
Mouse ML gets brain transplant of the killer but Life on Mars ML goes into coma then dreams the world as a nightmare

The background is a detective story plus thriller, the MCs are kind of cold and unapproachable by most people, they both deal with an almost Impostor's Syndrome situation over and over again (except they don't doubt themselves, just don't fit in, for reasons).

There's quite a bit of similarity between the endings of the two dramas, too (can't tell more in order not to spoil them.)

Also, the acting is through the roof - you've seen the male leads together (Lee Joon Gi and Jung Kyung Ho) in another rather good drama, Time Between Dog and Wolf, and they nailed it there, too.

Em de volta a 1989, o protagonista volta no tempo antes de seu nascimento e precisa descobrir como voltar ao seu ano. É muito engraçado, tem romance e viagem no tempo.

Really hard to make a recommendation without spoilers...
Both:
-Have an in-depth mystery
-Focus on the mind/background of the serial murders and their influence
- Are mature and involve some deep thinking
- Touch the problem of being a child raised in an abusive/ 'murderer' family and get a bit in depth with it
- Can give you lifelong lessons if you listen carefully
- Do not use common and cheap drama moves, so its a bit refreshing
- Do not have a lot (to any) romance

Just watch it. You wont regret i swear. Same vibes. Same actor. Good writing. And just a very good drama in general.