In a small saucepan over medium heat, cook blackberries, sugar for 5-10 minutes. Stir and mash blackberries. Add cornstarch, mixing well. Strain mixture through a mesh strainer into a clean bowl. Discard solids. Cover and chill puree.

In a medium saucepan over medium heat, cook whole milk, 1/2 cup heavy cream, sugar, salt and vanilla. Stir occasionally. When mixture begins steaming and bubbling around the edges, slowly drizzle into beaten yolks, whisking continuously. Pour egg mixture into saucepan. Continue cooking until mixture coats the back of a wooden spoon.

Add remaining 1 cup heavy cream to a medium bowl, pour warm custard through a clean mesh strainer into remaining heavy cream. Chill over an ice bath. Cover and cool completely before churning, 4-6 hours or overnight.

Churn according to manufacturer's directions. Layer ice cream and drizzles of blackberry puree in a freezer safe container. Cover and freeze until solid.