I second Nobuta Wo produce, Heartless City, warrior baek dong soo and Gokusen series
Other recommendation:
Nirvana in Fire - mainly centered into political machinations and strategic retributions plans but the bromance is super real in this drama. So much goodness and awesomeness in the bromance between all the male characters. And just over-all BEST drama ever!
The Disguiser - a must watch bromance trifecta of the 3 male leads. (Same main leads as nirvana in fire). And so much awesoness period war drama.
Last Match (1994) - realistic and reviting bromance and rivalry rolled into two friends as they strive to dream, love and follow a path that is uniquely their own.
Misaeng - office centered with bromance and comraderie at its finest. So much realism and life lessons in this drama
Awl - another bromance and office comradarie drama that is a must watch
Gentlemen's Dignity - from the writer of DOTS and Goblin, so there is a bunch of romance. But the bromance is just as good as the other 2 dramas
Reply series - bunch of bromance in all its series (1997, 1994 & 1988)
Pride - one of KimuTaku's drama, so its a must watch.
Bad Guys
A story of a Man
Rookies
Tokyo Dogs
Black and white
King 2 Heart