Also, in my experience, I haven't been able to learn anything "for real" without using it on a real project.
But there is nothing to show me if I correctly handle my prod-server updates (Now I upload, move, restart)
My testing is very basic.
And there is a general feeling of lack of infrastructure.
I would love to learn how to do a few-man-year project (from infrastructure's point of view)
Have you got any hobbies or interests? Why not create a website dedicated to your hobby/interest? That way it'll be something that you'll be able to run over the course of a few years.
Start with a small website, and slowly build it up. Add more features, then tweak them. Find out why it's loading slowly. Read a few books on website that scale too.