I have been to Cookiez on Mill many times and my only regret is not trying it sooner. Cookiez has a wide variety of desserts, including Italian ice, milk shakes, ice cream, fresh lemonade, and fruit smoothies.
While all of its desserts are excellent, the shop is most famous for its ice cream cookie sandwiches. A sandwich entails the combination of one or two large cookies (~4-inch diameter) and 2-3 scoops of ice cream. These massive sandwiches come in half (one cookie cut in half, with ice cream between each half) or whole (two cookies, one on top and one on bottom) sizes and are great for sharing. You can choose any of the several available cookie and ice cream options to make your own custom dessert. I recommend the combination of a white chocolate chip almond cookie with mint chocolate chip ice cream.
The prices are quite low. A discount is also offered to ASU students and people who work on Mill. The owner is very friendly and always in a good mood.
Pass on by the chain stores and stop in to Cookiez. You won't regret it.