In a medium saucepan, combine blueberries, sugar, cornstarch, lemon juice, and water. Cook over medium heat for 5-7 minutes until blueberries burst and mixture thickens. Let cool in the fridge for 1-2 hours.

In a large mixing bowl, beat together sweetened condensed milk, cream cheese, and vanilla extract until smooth and creamy for about 3-4 minutes.

In a separate bowl, whip heavy cream until stiff peaks form, about 3-5 minutes. Gently fold whipped cream into the cream cheese mixture until no white streaks remain.

Gently fold in graham cracker pieces, reserving some for topping, ensuring even distribution without overmixing.

In a loaf pan, layer a third of the ice cream mixture, followed by a third of the cooled blueberry compote, swirling gently. Repeat twice more, finishing with graham cracker pieces on top.

Cover the loaf pan with plastic wrap or lid and freeze for at least 4-6 hours until firm.