Place all the ingredients for the strawberry ice cream into a blender and puree until smooth. Taste and adjust sweetness to your liking.
Pour into an ice cream maker and churn until the ice cream is starting to set. Meanwhile combine all the ingredients for the cheesecake swirl in a medium bowl. Use a hand mixer to combine well. Taste and adjust sweetness to your liking. Swirl the cheesecake mixture into the strawberry ice cream.