This quest can be acquired as soon as you enter The Winter Palace during Trespasser. To begin, speak with Cullen, who can be found in the south east of the courtyard. During the brief cutscene, Cullen will mention that he’ll find some overpriced Orlesian dog treats for his new-found friend.
Note: This is an unmarked quest, which means it will not appear in your journal. Instead, you will need to find the dog treats throughout the courtyard without any indication of their location (see the map below for locations).
If the Inquisitor failed to persuade Cullen to stop taking lyrium, you will not be able to acquire the quest from him. Instead, you will need to wait until after the first meeting of the Exalted Council, at which point you will be able to explore the courtyard and find the treats.
There are 10 expensive dog treats in total. When you near their location, you will be able to use the search function to hone in on them. Once all 10 have been collected, return to Cullen and place them in the basket beside him. You will need to place each one individually, and each provides a bonus to your stats based on your class.