Ok, we ate there on opening weekend with one vegetarian and one that is cutting back on meat consumption.
Here is how it works:
First, you will need to email
DLR.Special.Diets@disney.com and let them know the number of people in your party, the dining times and locations, how many have dietary needs and what the restrictions are.
When your server comes to take your drink orders, inform them of the special dietary needs if they are not already aware (some times this gets to them, sometimes it doesn't).
At Carthay Circle the chef may very well come out to discuss it with you or your server will ask what kinds of foods you enjoy and will talk it over with the chef, who will come up with some options for you to choose from. The price range will be similar (in our case slightly cheaper) to the rest of the menu.
We had the opportunity to speak with the Chef and asked why there were no vegetarian options listed on the menu and he stated that it was done intentionally to ensure that he could work with those with dietary needs to get them something that they would truly enjoy. So, there is no set vegetarian or vegan menu items and honestly, this is a good thing as you end up with an amazing dish. In all honesty, I had the braised lamb pasta and my wife had a vegetarian pasta and I think I liked hers better (although mine was amazing as well)
If you would like to see my review, you can do so on Yelp at:
http://www.yelp.com/biz/carthay-circle-restaurant-anaheim#hrid:9Z4eJv-DiFWGUYX0BrGvVw
Here are pictures of the Vegetarian dishes:
So, my answer is yes, as a vegetarian you can go and have a great meal, I am sure a vegan could as well, but that wasn't an issue for us. Do not let the fact that there are no vegetarian/vegan options listed on the menu deter you from going, it was done this way to give you an opportunity to get something better than you would get if there were set items on the menu.
The service is beyond incredible, but be sure to arrive a bit early for your reservation and enjoy the lounge, we had just sat down in the lounge and asked for glasses of water when we were informed our table was ready.
The WOC tickets are almost worth the cost of the meal alone, you can indeed arrive as late as 15 minutes before the show starts and get a good spot, even if you have a special need, they will do everything they can to accomodate you.