Combine blueberries, 0.25 cup granulated sugar, and lemon juice in a medium saucepan. Bring to a gentle simmer over medium heat, stirring occasionally, and cook for 8-10 minutes, or until the berries have burst and the sauce has slightly thickened. Mash some of the berries with a fork if you like a smoother consistency. Remove from heat and let cool completely, then refrigerate until thoroughly chilled (at least 1 hour).

In a large mixing bowl, using an electric mixer, beat the softened cream cheese and 0.75 cup granulated sugar until smooth and creamy, about 2-3 minutes. Make sure there are no lumps. Gradually beat in the cold heavy cream, cold whole milk, vanilla extract, and salt until just combined. Don't overmix; you just want it smooth.

Cover the cream cheese mixture and refrigerate for at least 4 hours, or preferably overnight, until it's very cold. This is crucial for achieving a good ice cream texture.

While the base is chilling, in a small bowl, combine the graham cracker crumbs and melted butter. Stir until well combined. For an extra crisp crumble, spread the mixture onto a small baking sheet and bake at 350°F (175°C) for 5-7 minutes, until lightly golden. Let cool completely, then refrigerate until ready to use.

Pour the thoroughly chilled ice cream base into your ice cream maker and churn according to the manufacturer's instructions, typically for 20-30 minutes, until it reaches a soft-serve consistency. During the last 5 minutes of churning, gradually spoon in about half of the chilled blueberry swirl and about half of the graham cracker crumble, allowing them to mix in slightly.

Transfer the churned ice cream to a freezer-safe container. Dollop the remaining blueberry swirl and graham cracker crumble over the top and gently swirl them in with a knife or spoon. Cover tightly and freeze for at least 4-6 hours, or until firm, before serving. This allows the ice cream to harden to a scoopable texture.