Composting

My understanding is a lot of "greens" eventually become "brown". Green leaves when they dry up would switch to a "brown". Same with dead grass.

With that in mind I tried a very lazy process of only adding greens for a continual process. My first addition to my pile this year was grass clippings. They still haven't really broke down.

Is my approach fundamentally flawed? Or is there something I'm missing to improve the process?