01 - Combine blueberries, 1/4 cup sugar, and 1 tablespoon lemon juice in a small saucepan. Cook over medium heat for 5–7 minutes, stirring frequently, until berries burst and the mixture thickens slightly. Remove from heat and allow to cool completely.
02 - Beat the softened cream cheese in a large bowl until smooth. Add sugar, lemon zest, lemon juice, vanilla, and salt. Mix until well combined and creamy.
03 - Gradually whisk in the milk until the mixture is smooth and no lumps remain. Add heavy cream and continue whisking until fully incorporated and homogeneous.
04 - Pour the mixture into an ice cream maker and churn according to the manufacturer's instructions, typically 20–25 minutes, until it reaches a soft-serve consistency.
05 - Gently fold graham cracker crumbs into the churned ice cream. Transfer half to a freezer-safe container, spoon half the cooled blueberry swirl over the top, and lightly swirl with a knife. Repeat with remaining ice cream and blueberry swirl.
06 - Cover the container tightly and freeze for at least 6 hours or until the ice cream is firm enough to scoop.
07 - Let the ice cream sit at room temperature for 5–10 minutes before scooping to soften slightly for easier serving.