Ingyin Nwe

The two times I went in it appeared only one of the staff members spoke English. This would have been fine as the menu is in both english and burmese but the other staff seemed very vary of coming near! The refills were greatly appreciated and I actually had to beg for them to stop during my first visit as I was so stuffed! It's very basic rice or chapati with three dhal based curries. On my second visit the English speaking waiter was on a break and so no one actually refilled my plate, portions are good but this was a little annoying as it's a big reason to go there for the refills hehe. The New Delhi on the same street about 5 minutes before does a similar thing but with 5/6 dishes. A bit crazier but cheaper at 1200 to ingyin's 1500 and you get more variety. Both featured in lonely planet

I had a vegetable chapati plate for 1000 kyat when I was there. They confirmed to me that no ghee or butter was used in the dish at all and I hope this info was accurate. It was delicious and they refilled my plate. What bothered me was that smoking was allowed and facilitated in the restaurant, however as it was an open room, it did not affect me hugely.
Considering vegan options are limited, especially if you want real
Indian Food, I'd still recommend this place.

Just confirming what's said below - there's a whole menu full of non-veg options, but there are also awesome dosa, nan, or roti sets (800 Kyat and up) and an all-you can eat vegetarian Thali (1200 Kyat) where, just like in southern India, the waiters wander around with buckets of curries, sambars, and so forth, and ladle them generously onto your plate.

About two thirds of their menu is actually non vegetarian...
Also there are a couple of similar Indian restaurants nearby.
But despite that I think this is one of the best options for vegans in central Yangon.
The food is good, it's cheap and the staff is friendly.
You might also try one of their delicious Thosay (or dosa as they would usually call it in most of southern India)

This place became my mainstay whilst in Yangon city: for !000 kip (under $1.50 AUD via local exchange rates), they offer an unlimited veg thali which includes rice; several veg curries; pappadam; and naan or roti. I've a pretty large appetite, but found that I couldn't get through their pappadam or breads, and had to beg the over-enthusiastic staff to stop refilling my platter (which they tend to do every time you take a spoonful).

Not sure about vegan options, as - whilst a committed vegan for three years - I've found my veganism becoming more 'flexible whilst in SEA, and grateful to obtain a *veg* meal without fish or shrimp sauce or paste, meat broth, egg etc. (cultural and linguistic barriers making it very difficult)...great place, super-friendly staff, great prices and location; highly recommended!