In a saucepan, cook the blueberries, sugar and lemon juice over medium heat until the sugar has a jam-like consistency. Remove from the heat and transfer to a heat-proof bowl. Allow to cool completely.
In a separate bowl, whisk the eggs and sugar until light and frothy.
Heat the milk and cream cheese in a saucepan to boiling point. Slowly whisk the cream cheese mixture into the eggs and sugar. Allow to cool.
Transfer the mixture to an ice cream churner and churn according to manufacturer's instructions.
Once churned, scoop out a few spoonfuls into a container, place a few teaspoons of blueberry compote and continue to layer.
Place in the freezer until ready to serve.