There's a reason why Yelpers are singing praise for Haji-Baba. The few skeptics must have not taste for good food or must come from Middle Eastern families and hate anything not cooked by their mothers and grandmothers.
Haji-Baba is one of the better Middle Eastern eateries I have had the pleasure to try. Not just in Tempe but anywhere (including NYC and Toronto). I had the shish kebab plate that included generous portions of rice and salad along with the chunks of lamb. It came with a pita slice too.
It's an unorthodox place. You're given a ticket that you present to the cashier. Anything you may purchase from the grocery side will be added. If you cook you might enjoy the wide variety of spices and other items for sale. They even sell a few edibles from Croatia and Serbia.
Be sure to try the baklava. They have a few varieties. I tried the Queen Baklava and it was fantastic. One of the best I've had.