In a small saucepan, combine the fresh blueberries, 1/2 cup of granulated sugar, and lemon juice. Cook over medium heat until the blueberries burst and the mixture is syrupy, about 5-7 minutes. Remove from heat and let cool.
In a large mixing bowl, beat the softened cream cheese and the remaining 1/2 cup of granulated sugar until smooth and creamy.
Add the heavy cream, sour cream, vanilla extract, and salt to the cream cheese mixture. Mix on medium speed until well combined and fluffy.
Gently fold in the cooled blueberry mixture into the cream cheese mixture, being careful not to fully blend; you want swirls of blueberry throughout.
Stir in the graham cracker crumbs to add that cheesecake element to the ice cream.
Pour the mixture into an ice cream maker and churn according to the manufacturer's instructions until it reaches a soft-serve consistency.
Transfer the mixture to an airtight container and freeze for at least 4 hours or until firm.
When ready to serve, allow the ice cream to sit at room temperature for a few minutes to soften, then scoop into bowls and garnish with extra blueberries.
Notes
Allow the ice cream to soften before serving for easier scooping.