Place blueberries and 1/2 cup sugar in small saucepan. Cook on medium heat until the sugar dissolves and berries start to split. Mash the berries slightly and add cornstarch. Cook until thickened. Cool completely.
Place half & half, cream, vanilla and remaining sugar in a bowl. Mix until thoroughly combined
Put the cream mixture into your ice cream maker. Attach stir stick to ice cream lid and place on ice cream maker.
Add ice and rock salt to the mixer bowl.
Turn the mixer onto speed 4 for about 20 minutes.
Add ice and rock salt as needed.
Place ice cream in a ice cream container, pour cooled blueberry sauce over the ice cream, and layer crushed graham crackers on top. Swirl the layers together gently.