In a medium saucepan, mix together blueberries and sugar.
Cook over medium-low heat, stirring occasionally, until the blueberries are soft and the mixture is thickened, about 10 minutes.
In a separate bowl, whisk together the cream, milk, cornstarch, and vanilla extract.
Slowly add the cream mixture to the blueberry mixture, whisking constantly.
Bring the mixture to a simmer, whisking constantly, until the mixture is thick and creamy, about 5 minutes.
Remove from heat and cool completely, about 30 minutes.
Pour the cooled mixture into an ice cream maker and churn according to manufacturer's instructions.
Serve immediately, or transfer to a freezer-friendly container and freeze for up to 2 weeks. Enjoy!