I was staying in Mesa for awhile and found Cornish Pasty Co on Happy Cow and decided to give them a try. I ordered takeout as the restaurant was full (on a Wednesday evening) - the 'good times' atmosphere within was palpable.
I tried a couple of different pasties and a desert one as well. They were very tasty and very filling. I found the price to be more than fair.
The best part is their flexible menu with many of their pasties which can be vegan-ized upon request. The menu is very straightforward about this which is much appreciated.
Look to make a reservation and don't hesitate to check this place out. I'd say it's pretty unique, the food is good and they show that they care about vegetarians and vegans.
Cons: Can be crowded, loud