If you're vegan ask for Niy Niy. He speaks excellent English and knows what vegan means.
We loved The Moon. We ate there all four days we were in Bagan. Terrific setting, expansive menu and helpful staff.
We especially recommend the coconut shakes made with coconut water, the lentil soup and most everything on the menu ;-)
Our only complaint would be that we had trouble eating there as vegans. We ate there several times and more than half of them things we ordered without milk, etc. still came with animal products. They managed to sort out the issues eventually, but it could have been much smoother.
Definitely recommend this place for a unique experience and for supporting a good cause.
Cons: Challenging as a vegan, Costs a bit more, Allows smoking