Beat together the cream cheese and sugar until fluffy and smooth. Add the egg and vanilla, mix until creamy and set aside.

Bring the milk to a boil over medium-low heat. Remove from the heat and add a quarter cup of the milk to the cream cheese mixture and mix until combined and smooth. Continue with 2 more quarter cups of milk and then add the entire mixture back to the pan with the rest of the milk.

Stir over medium-low heat until thickened slightly (should take around 3 minutes). Remove from heat, strain mixture, and let cool 10 minutes.

Combine the zest, heavy cream and cream cheese mixture together. Pour into your ice cream machine and freeze according to manufactures instructions.

When ice cream is thickened and finished freezing, slowly pour in the blueberry lime syrup and let ‘swirl’ a few times in the machine before turning off. (You can also do this by creating layers of the ice cream to a container and adding the syrup between layers , then swirl with a knife a few times.)

Combine first four ingredients in a sauce pot. Whisk together the water and cornstarch and add the sauce pot. Turn the heat on to medium and let simmer until until thickened, about 10 – 12 minutes.

Let cool completely