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 mixture thickens slightly. Remove from heat and cool completely.
02 - Beat cream cheese in a large bowl until smooth. Add sugar, lemon zest, lemon juice, vanilla, and salt. Mix until well combined.
03 - Gradually whisk in milk until smooth. Add heavy cream and whisk until fully incorporated.
04 - Transfer mixture to ice cream maker and churn according to manufacturer's instructions, typically 20–25 minutes, until reaching soft-serve consistency.
05 - Gently fold graham cracker crumbs into churned ice cream. Transfer half to freezer-safe container, spoon half the blueberry swirl over top, and lightly swirl with knife. Repeat with remaining ice cream and swirl.
06 - Cover container and freeze for at least 6 hours or until firm throughout.
07 - Let ice cream sit at room temperature for 5–10 minutes before scooping for easier serving.