Ok so I have some actors that are not necessarily "ugly" but do not have typical flower boy idol look (but i still find them pretty handsome) (though i'm not sure if this is what you are looking for)
Lee Min Ki in Because This Is My First Life
Seo In Guk in Reply 1997 (honestly, i find adult SIG really handsome but when he was younger he wasnt this hot. hes still cute though)
Ryu Joon Yeol in Reply 1988 (i think hes very handsome but has different bone structure which makes him look different so there is that...)
Lee Dong Hwi in Drama Special Season 7: The Red Teacher (this is just really good drama special lol)
Yoo Ah In in Chicago Typewriter (idk his aesthe in the drama just wasnt my thing)
But if you are looking for "older" renowed actor, check out Ma Dong Seok - i think he's very good but does mainly crime dramas
+1 My Mister