In a medium saucepan over medium heat, combine blueberries, sugar, and lemon juice. Bring to a simmer and cook, stirring occasionally for 5 to 7 minutes, or until blueberries have burst and the mixture is thick. Remove from heave and cool completely, chilling in the fridge if needed to cool faster.

Add cream cheese to the bowl of a stand mixer fitter with the paddle attachment. Cream the cheese lightly, until just turning creamy and smooth. Add in milk, cream, sugar and salt and continue to blend until smooth.

Add the cream cheese ice cream mixture to your ice cream maker and churn according to the manufacturer’s instructions. For the Cuisinart Fruit Scoop machine, churn for 15 minutes.

Spoon in the blueberry compote, add in the graham crackers, and churn for 1 additional minute. Pour the mixture into an airtight container and freeze overnight before serving.