Marriage Contract is a very good one to start with.
Go Back Couple was very lovely.
Temperature of Love is a very good one with the mature romance.
Will You Have Dinner with Me is another good one.
Will I consider Kiss Sixth Sense a part of this too?

And I almost forgot You Are My Spring. It's the one I'll tell you to watch first before the listed above. The addition of their ages is 72. And I tell you, you'll enjoy it.

On the Way to the Airport
I know a lot of people don't like to watch dramas with 'affairs'. But this was a very well done drama. It really did focus on characters, and how marriages fall apart over time and how people change. It really was a well done drama.
Her Private Life - Again, a drama with mature leads acting like adults! whats not to love.

I'm not big on romance dramas, but "QUEEN IN-HYUN'S MAN" won me over. The chemistry was great, and I liked the story enough to overlook the imperfections.
I've always had a soft spot for the historical Queen Inhyun and how she died childless and unloved, so this drama gave her a happy ending.
Fangirling over Kim Bung-do made it a fun watch.

I thought “I need romance 3” was good :)

I haven't watched a lot in this category, so I'll definitely check back to consult these recommendations too!

The one that comes to mind immediately for me is Chocolate. It's a lovely slow-burn romance that has a lot of damaged people healing along the way. And such glorious sequences of food being prepared.

Greatest Love
Bubblegum
Jealousy Incarnate
Nine
Miss Korea (the seconed love-line)

Most of my favorite shows feature thirty-something characters but most of them don't look distinctly different from late-twenty characters.

Hyena - late 30s ML, early 40s FL. This one is a RIOT! Acting, chemistry, jokes are insane. Both leads are rather... questionable in many aspects, and imo drama should've been a bit longer to give a proper conclusion to all the issues between the OTP, but it's still a fantastic watch if you can stomach legal dramas. And kinda suspend your disbelief over ML still carrying the torch for FL after a certain truly dickish move she pulled on him. Personally I would've RUN if I were him, but some folks just love the pain and challenge)))

Hmm... in Another Oh Hae Young both leads were over 30, right? Very mature one indeed - nearly all adult problems are covered here one way or another.

My favorite one is "Love Affairs in the Afternoon". And I second jerry with You Are My Spring and Go Back Couple.

But I also enjoyed:
18 Again
When My Love Blooms
Flower of Evil
It's Okay That's Love
Once Again (weekender)
Be My Dream Family (daily drama)
Cunning Single Lady
20th Century Boy and Girl
My Liberation Notes
Matrimonial Chaos

There's also "Tomorrow With You". The show is... but the couple is great. They were adorable.

I propose the name “aju” romance (ajumma-ajusshi) and select The Man who Didn’t Want to Marry/He Who Can’t Marry. All the zaniness of hate-to-love at any age but with the lovely mature actors Ji Jin Hee and Uhm Jong Hwa.

Also, Marriage Not Dating although they were a bit on the young side.

A topic near and dear to my heart! As a rule, I am bored by romcoms featuring teens and 20-somethings. I find relationships between people who’ve “been around the block” at least a few times so much more interesting. Among my favorites (some of which have already been mentioned):

Because This Is My First Life
Fated to Love You
Hyena
Search: WWW
Crash Landing on You
Kill Me, Heal Me
The Master’s Sun
Oh My Venus
A Piece of Your Mind
Greasy Melo
You Are My Spring
When the Camellia Blooms (Not sure…is the ML in his 30s?)

I was thinking all the Hospital Playlist friends. Dear my friends as I think the daughter is in her 30’s and I am sure there is a budding romance amongst her mum’s friends.

Lee Chung-ah and her persistent office colleague Jung Joon-won in VIP. One of the few romance subplots in a serious drama that I don't FF through. My favorite mature relationship stories are about romance lost -- adultery dramas -- so I guess they don't qualify.

The main romance in Five Children was nice.

Alone In Love

I'm noting all these recommendations. But while I do agree 30-somethings are more mature than teen/20s, I would have defined middle-age as 40-60, esp. given how long people live now. Of course, everyone's definition of middle-age varies. But I think romances in that age range are even fewer. Many of the recommendations here are for 30-somethings.

The Beauty Inside
My Unfamiliar Family
Oh My Baby!

I agree with @babylilo! I too wish there were more mature dramas! There’s usually an interesting backstory for folks who have been around the block. There’s depth.
Probably because it’s a recent watch, but I really enjoyed LOVE TO HATE YOU. The leads are 36 and 41, and even the subject matter is mature. I read somewhere that many people complained that the leads were too old. Whatever. First of all, I don’t think 41 is old. Secondly, while there’s no denying the beauty of youth, older folks know how to take care of business.

It's sad but the characters who are around 35-4 years old often are in either family dramas either majkang dramas.

39 could have been so good with romance between adults and friendship >_<

Oh My Baby was really good until the writer fell in the usual clichés.

One Spring Night was interesting with the ML being a single parent.

I didn't watch Love Affairs In The Afternoon but I liked the Japanese version.

I've been waiting for a post like this and I'm DEFINITELY writing down suggestions. High school and young love dramas certainly have their places in my heart, but I'm all for love among the *older* crowd.

I see this post as one addressing couples in the 30+ age range. IMHO, the 30s are not truly considered middle age, but I get the gist of what you're saying and I approve!

The drama that immediately came to my mind was When My Love Blooms. It was a good story about an older couple's second chance at love, but had flashbacks of their younger years as well. (This, to me, is the best of both worlds!)

I also enjoyed Hometown Cha Cha Cha. It had a great storyline as well (Du Sik's backstory broke my heart!). To be honest though, if Kim Seon Ho is starring in a drama, I'm definitely watching.

These have characters who are at least in their 30s, so more mature if not middle-aged:

A Gentleman's Dignity
Bossam: Steal the Fate
I Do, I Do
Secret Love Affair

Not the greatest dramas, but still...

Love in Contract
Now, We Are Breaking Up
Thirty-Nine
The Woman Who Still Wants to Marry
Where Stars Land

Adding some that haven't been mentioned:
City Hall - an oldie but goodie
Live Up To Your Name
Mystic Pop-up Bar

With the following dramas, I'm not sure of the characters' ages, but they're definitely not teens/early 20's:
My Name Is Kim Sam Soon
She Was Pretty
Touch Your Heart
What's Wrong With Secretary Kim

If you're up for a Chinese drama, then You Are My Glory fits the bill :)

A Witch’s Love is pretty good at showing a middle aged woman’s POV in romance, and I like that it did so unabashedly. The writer really presented FL with a sense of pathos. The last minute of Love to Hate You really ruined the show for me, by turning FL into a joke. She wasn’t tough in that last scene, but a harpy. Badly done!

Not a perfect series, but I liked the concept and the acting is good.

Love Rain
When My love blooms
Recipe for Farewell
20th century Boy and girl