As in life itself, we never stop moving towards this (emotional maturity) or we shouldn't at any rate. Sadly some do and stagnate. It's a journey that we won't fully complete I think. But we can grow in EM and reach a point of contentment I hope. I think its a combination of confidence, love of ones self, emapthy, and just plain control of emotions (instead of them controling us) that give us EM. It's also about reacting in a positive and constructive manner to the emotions of others. I don't think you have to restraint and bury emotions to achieve EM, instead you must reconginze your own personal emotions for what they are and what they do and mean to you. And act accordingly.
If you are "emo", chose the proper time and place for strong emotion. If you are "cold" you still have feelings. Work on feeling comfortable with them. A wise man once said "this most of all. unto thine own self be true". This is the real key to EM. Take what you have and embrace it. Fe..errr..love does make the world go round. Combine it with control and you can do wonders.