Can we define craving without mentioning self?
An example is there in the paticca-samuppada itself.


  Vedana Paccaya Tanha


Feeling gives rise to craving. 
So in reality there's no "I like icecream". 

It should be 


liking arises due to taste
liking arises due to sight
liking arises due to sound etc. 


There's no practicing Anatta. You practice mindfulness and the Anicca, Dukkha, Anatta natures are revealed. Practicing the noble eightfold path leads to the cutting off of craving and cessation of suffering. Mindfulness is a part of the noble eightfold path.