top of the head Our Blooming Youth

The first one that comes to mind is The Crowned Clown. Beanies are divided on this drama, but they are largely not divided on the fact that Yeo Jin-gu was incredible in his dual roles. The two roles don’t have too much interaction, but they do meet, so this fits the stricter requirement too. I really loved this drama and found it really intense to watch - such high stakes!

Another great one is My Holo Love - this one is fun because one of the characters is an AI interface that the ML (same actor) created. The FL meets the AI and then later meets the ML and understandably gets them mixed up. It’s a quick, sweet drama that actually has a good use of face-blindness.

A Time Called You probably also counts because there are doppelgangers galore in this drama (it’s part of the setup). Not as many of them meet here, but often the actors’ characters are very different from one another, and it can be fun to pick up on the subtleties (or in some cases, the not-so-subtleties!).

The last one that I can think of is The King’s Affection which doesn’t have as much of this, but the child actor who plays the young FL also plays her twin brother and they have a fun encounter (and more in flashbacks I think). Not so much when they are adults for *kdrama reasons*, but the FL is a really cool character and Park Eun-bin plays her incredibly well (as is to be expected).

Kim So-hyun in School 2015, playing identical twin sisters with very different lives.

Only tangentially relevant because they're films rather than drams and the characters don't interact, but Son Ye-jin played the female lead and her mother 30 years in the past in The Classic.

Additionally, without being too spoilers, Jung Ryo-won had distinctly different traits while playing the same character in Two Faces of my Girlfriend

The King: Eternal Monarch had a clutch full of people.
- Woo Do Hwan
- Kim Go Eun
- Lee Jung Jin
And quite a few more.

Lee Mi Sook in Greasy Melo (Wok of Love).

If A Time Called You counts then perhaps so will Lovely Runner (Carry Sun-Jae And Run) and also Atypical Family!?

The first part of Arthdal :p Personaly, I thought Song Joong-ki did a better job to play the twins.

Yeo Jin Goo was great in The Crowned Clown like @jls943 wrote.

Hyun Bin did in Hyde, Jekyll, Me but it was the same person with 2 different personalities, so they didn't meet. And the whole drama was bad...

Seo Kang-joon as a person and a robot in Are You a Human?

Yoon Hyun-min as a person and a AI in My Holo Love too.

Yoon Park had a duel role in You Are My Spring.

DESTINED WITH YOU had the same actors of the current timeline enact different roles in a preceding timeline (so they don’t meet… „themselves“).
Same with THE STORY OF PARK‘S MARRIAGE CONTRACT.

I remember yang se Jong played a dual role in a series called Dual/duel. They were estranged brothers. I don't remember the exact story but it involved human cloning and one of the brothers is an anti hero. I remember enjoying it while it was airing.

Chae Soo-bin in I’m Not a Robot is something I enjoyed a lot.

Does Ji Sung in Kill me Heal me count?

Uhm Ki Joon in Defendant

Chae Soo-bin in I am not a Robot.

Now that the topic has come up, im suprised it doesnt happen that often in makjang dramas

First one that comes to mind is Ji Sung in Adamas!
For characters that dont interact Ji Sung in Kill Me Heal Me also works.

I am not a robot
Are you human too?

Does Psychopath Diary count? I'd say it does! 😂
-->This drama is a favorite of many @britney. Not me, but many others.

Also, while the actors only play themselves in one (?) of the past lives, See You in My 19th Life also has this trope--and you could say that they interact.
-->This show is much better as a binge-watch than it was live. @claire2009 is leading a Fan Wall Community Watch on it, and I am convinced it's better than the reviews/recap comments might let on.

Seo In-Guk in High School King of Savvy.

I am a little confused why probably the best of the lot Yang Se-jong’s OCN drama DUEL (2017) is still available. He gave an incredible performance of really 4 roles: good clone, bad clone, clone creator and (for story purposes) the good clone imitating (or trying pass off) as the bad clone.

Train
Switch
Your Honour
Two Cops
Bride of the Century
Room #9
What Star Did You Come From
Ghost
Mask
The Light in Your Eyes
Brain Works

There are so many 😄

Ji Sung : Adamas.

He played both characters with clear distinction that you can tell who is who, even when they are playing a fast one on their enemies.

Ryu Hye-young : Law School.
She plays Kang Sol A and Erica. There's more Kang Sol A than Erica here.

Yoon Park : You Are My Spring.

Yoon Park plays a twin here. The one we spend most of our time with is the Doctor Chae Jun. No need for intros. But then there's the other twin I spent so little time with but made an impression, the other twin Choi Jung-min. This drama subverted the power trope in twin relationships, highlighting the insecurity of the supposed "power" twin.

Song Joong-ki: Arthdal Chronicles.

Song Joong-ki plays not 2 but 3 characters in Arthdal Chronicles 1. The third character is a pseudo one. But color me intrigued and wow when the pseudo character was revealed to be one of the twins, Saya, masquerading as a woman.

Choi Myung-bin : The King's Affection.
If you think Song Joong-ki played feminine Saya to a tee in Arthdal Chronicles 1, Choi Myung-bin plays male and female twin in TKA, an impressive performance in the midst of accolades due to TKA. She was a revelation. She disappeared completely into the male twin counterpart, you'd never tell she's female.

ADAMAS!!!
What’s better than Ji sung, it’s two Ji Sung!! There were plenty of scenes with both of them together.

Mr. Queen: Shin Hye Sun as both the queen and Jang Bong Hwan trapped in the queen's body.

In Hwayugi, Lee Se-young was both the lovable zombie Richie and the vengeful, centuries-old Ah Sa Nyeo.

Ji Sung in Adamas played twins
Lee Dong Wook in Tale of the Nine Tailed
Chae Soo Bin played two roles in I Am Not a Robot
Yoo Jin Goo is amazing in The Crowned Clown
Ji Sung played multiple roles in Kill Me Heal Me to great success

Yeo Jin-goo's performance in CROWNED CLOWN is memorable to this day. He should have gotten the Best Actor Baeksang award for this performance.

Reborn Rich
Oh My Ghostess
49 Days

In terms of ones people haven't mentioned yet, Resurrection does this, although the interaction between the two characters is limited. The Best Hit also does a version of this, although it's technically the same character meeting himself in an earlier time period. If you want to venture outside of K-drama, one of the most interesting takes on this trope I've seen is the Taiwanese show Someday or One Day where multiple actors play multiple characters.