If you scroll down to the bottom of this webpage and then type "harvest onions" in the search box, you will get a wealth of information on this subject.

I have not waited for mine to completely go brown, mostly because I am eager to use the spot for transplanting something else. It sounds like you will have to stagger your harvest. Your question actually does not come up that often, and the answer is not as straightforward as I would have thought.

http://forums.gardenweb.com/forums/load/allium/msg0720492514944.html
is a thread started six years ago that has excellent advice.

My favorite answer is the first response in the thread linked below (http://forums.gardenweb.com/forums/load/allium/msg0712253021698.html)

It would be nice to hear more experiences.

Best of Luck!

Here is a link that might be useful: http://forums.gardenweb.com/forums/load/allium/msg0712253021698.html

I harvest my onions when the neck (where the stem meets the bulb) is very soft when pinched. At this stage I believe the bulbs have stopped growing, even though the leaves are still green.

TomNJ

Onions still put on more growth than you can imagine from the time that the first one falls to when they all have fallen. This usually takes only a week or 2.
The number I read was something like 10% of their growth happens in the last few weeks. So usually I wait till about half have fallen on their own, then I kick down the other half, wait a week and dig them.