MLB, I see you have used shiitake mushrooms. That's a real nice addition, gives the whole dish an exquisite flavour. If you can't find them fresh, dried version works, too, after soaking them for about half an hour. You can reserve the water to utilise it for risotto etc.
Personally my carrots go in first along with onions. They are pretty resistant to heat and takes a lot to get them to cook, so they also need to be sliced very, very thin with an extra sharp knife. (if your knife is short of extra sharp, they will fly all over the place!)
Broccoli are also tricky, I don't like them overcooked mush, nor semi-raw crunch. They need to be just at the right consistency. So I usually steam them first and add them at the last minute, just to coat the flavours.