Is It Possible to Get a Monolid/epicanthic Fold?

Can be done but leaves a scar. Usually not worth the trade off. I have reversed over-agressively done epicanthal folds. 

Your Korean heritage is something you are rightfully proud of and I must say you have the best of both worlds. Us Korean surgeons spend half of our lives making our traditional Korean eyes look more beautiful eyes like yours and although what you're asking for is technically possible I have to agree with the other surgeons that it shouldn't be undertaken for the reasons that; 
1) Such procedure can so easily go wrong and give you bad scars or something called webbing, either of which are difficult to fix once it happens
2) If that's the look you're after, so many great Youtube clips on make up by Korean makeup artists will give you such effect and more.
My daughter has eyes like yours, created by nature and I'm forever trying to recreate it. So enjoy, they're perfect.

The answer is basically no.  The scary thing is that someone might try for you.  I assure you, that will be a decision you will regret.  You are beautiful.  Now forget about the epicanthal folds.