Due to magic and Ice Queens unique anatomy her breast milk can be turned into ice cream. Ice Queen is force fed ice cream ingredients for the flavor of the day until she is are very full. Ice Queen has been injected with chemicals and aphrodisiacs to make her constantly produce milk to the point where her breasts have become huge and full of milk. Every time a customer wants some ice cream they just pull a lever assigned to her body and the machine that she's stuck in will vigorously milk her tits and until they produce delicious ice cream.
Ice Queen is trapped in the ice cream machine but is given breaks to rest and clean up.