In a large bowl, whisk together milk, half and half, sugar, and vanilla. Fill the ice cream maker with the mixture and run for 15-20 minutes.
While the mixture runs, combine in a mixer cream cheese, sugar, and vanilla. Then fold in the blueberries.
When the ice cream is done, swirl in the cream cheese mixture. Serve or freeze for later.
Tip: When making ice cream be sure to keep your cold ingredients in the fridge and your frozen ice cream insert in the freezer until you are ready to use.