In a medium saucepan, combine fresh blueberries, granulated sugar, cornstarch, lemon juice, and water. Heat over medium, stirring constantly until the blueberries burst and the mixture thickens—about 5 to 7 minutes. Once done, transfer your blueberry compote to a container and let it cool in the refrigerator for at least 1-2 hours.

Using an electric mixer, beat together sweetened condensed milk, softened cream cheese, and vanilla extract until smooth and creamy, about 2-3 minutes. In a separate bowl, whip heavy cream until stiff peaks form. Gently fold one quarter of the whipped cream into the cream cheese mixture, then carefully fold in the remaining whipped cream until just combined.

Spread one-third of the blueberry cheesecake ice cream mixture into a cold loaf pan. Drizzle one-third of the prepared blueberry compote over the ice cream, then use a knife to swirl it gently. Repeat this layering process two more times, finishing with a layer of ice cream. Cover the pan and freeze the ice cream for at least 4-6 hours.

When ready to serve, allow the ice cream to sit at room temperature for about 5-10 minutes for easier scooping. Serve in bowls or waffle cones, garnished with any remaining blueberry compote and reserved graham cracker pieces.