I loved My Name for the dark tone and main character. There are quite a few more mafia themed k-drama if you want more like it, but I think this show did it the best. Of course then there is the movie Parasite, you might already know it. I thoroughly enjoyed it and it's famous for good reason. Also I just remembered Extracurricular Activities. Another crime themed show, maybe a pattern for k-drama or just my tastes, but this one I really liked for the two main characters. They're competent, arguably evil, but still written believably imo.

Dramaworld was one of my entry points and I think it serves that purpose well.