What would be the most romantic thing I could do to win my ex back?

Well.Flowers would be good and a letter from the heart that says how much you want her back and how much you love her would probably make her melt, so go for the flowers and letter.

Considering the situation, probably the most romantic thing you could do is hand deliver those flowers.

Women, especially ex's, want guys to pay attention to them. Being in the moment with them is very important, but also remembering some of the details helps. Hopefully you remember her favorite kind of flowers. And no, not every woman enjoys red roses. But you hand delivering them, with a letter about how you feel and how you want the privilege to make it work. Talk about the things you've learned, how you have improved, how you will continue to improve, and how you need her to make it happen.

That, my friend, will definitely get the ball rolling.

Life isn't a Disney film, which is to say romance doesn't make women want to be with you. What you need to learn how to do is attract women. Check out The Game by Neil Strauss. That'll show you what's possible. From there read The Venusian Arts Handbook, Magic Bullets, and related material. Great primers on what makes attraction happen, as well as plenty of tips to make it occur.