My sister-in-law Maria had her birthday just recently and we took her to our favourite café, Baba Sus in Glen Iris, for breakfast. The co-owner of this café is a Japanese chef (you can read about her here !) and the menu has some Asian influence.
Paul and I always share two dishes, a savory and sweetie. We ordered a burger and the Hong Kong Style pancakes ;-) Their food never disappoints us, the staff are friendly and their service is great!
If you are traveling to Melbourne from somewhere else, it's not really an easy spot to visit though because it's a bit far out from the city (about 25min by train) and there's no tourist attractions around there, but if you live in the Eastern Suburbs of Melbourne, this is a must-go place. If you take your friends there, you can definitely impress them!