The Pros have given us some great inspiration for chipping or pitching out of a deep rough. So how do you hit this kind of shot? You've probably hit it many times actually, just most likely out of a bunker. Yes, the same technique that you'd use to get out of a bunker, you should use to hit the soft, high flop out of thick rough.
There are three main points to remember:
Set the ball forward in your stance, open the clubface. Just like a bunker shot, you want to hit slightly behind the ball and use the rough as a springboard to gently pop the ball out.
On the backswing, keep a quiet lower body. Most amateurs struggle with this, often straightening up in the back swing and shifting their low point of the swing. If you get too steep, you will slide right under the ball and the ball will not go far enough.
Fire through on your swing, maintain your spine angle, and fully rotate your hips. Your belt buckle should finish to the left of the target line.
The goal here is to get the ball on the putting surface, hopefully with a makeable putt. If you can get it close, that's an added bonus. If you can make it, well, that's amazing. But it certainly doesn't have to mean a big number. Play it like a bunker shot, commit to the swing and watch the ball float softly onto the green.